Ainur

One thing that some people end up asking themselves when the read or watch The Lord of the Rings for the first time is "what makes this Sauron guy such a big deal?" or "so what exactly is this Gandalf character?" The answer to that is that they are Ainur, which could basically be considered Angels created by Eru Ilúvatar. They are spiritual beings who were created from Ilúvatar's thoughts before the beginning of time, each having their own free will and varying levels of innate power. They sung the world into existence and shaped it afterwards, for good or bad. Some of them went into the world and were bound to it, these are the Maiar, and had physical form that Tolkein calls a 'raiment' (an archaic Norman word for fancy clothes) that they used to interact with the world; the Ainur have the ability change the appearance of these forms, but the more an Ainur becomes embodied in a particular form, the more they become locked in and limited by that form, and can even be destroyed and their spirits "disembodied," which is the closest thing to death a Maiar can experience. For the story timeline, see the Silmarillion, The Hobbit and Lord of the Rings articles in that order.

Eru Ilúvatar

While not an Ainur himself, and is barely involved in the legendarium beyond the Music of the Ainur and a handful of other events, it's worth mentioning him here. Eru Iluvatar lives not in Middle Earth or Valinor, but "Beyond the Circles of the World" in the Timeless Halls, with the rest of the Ainur who didn't enter Arda. As previously stated, he's the singular all-powerful being from which all other sentient beings originate, whether they be Ainur, Elf, or Man (and Dwarves on a technicality), as he alone possesses the Secret Fire, the source of free will and independent being. Its perhaps because of this that he takes a very hands-off approach with his creation, though not 100% of the time; while people can point to obvious interventions like allowing Beren and Luthien to return to the world of the living, or sinking Numenor, Ilúvatar also works in very subtle ways; multiple times in the Lord of the Rings, many coincidences, premonitions, lucky breaks, and chance encounters happen throughout. While one might be able to attribute them to the Valar individually or as a whole, none of them have as much foresight as he does, and a loooooot of shit had to go right just for the ring to end up with the Baggins family, for the Fellowship to form, for the ring to make it to Mordor, and for the ring to actually be destroyed in such a way that Sauron couldn't anticipate.

Valar

The strongest and most powerful Ainur to come to Arda and depending on how you look at them are either archangels or gods with a lower case g. There are thirteen in total, each one roughly corresponding to a particular "domain" analogous to Greek gods, though the Valar themselves do not claim to be deities of any sort (except for Melkor; more on him later). All the same, they're still highly respected by the Elves and Men of Dúnedain descent, and will oftentimes invoke their names in times of need.

The Valar ruled Arda from Valinor, aka the Undying Lands, from the beginning of time until the Second Age, when they relinquished control of Middle Earth to their creator Eru Ilúvatar, and Valinor became permanently separated from the rest of Arda.

They are:

• Manwë, King of the Valar and ruler over air and wind. Married to Varda, also Melkor's brother. The Great Eagles are Manwë's eyes and ears in Middle Earth. He is a very divisive character given the shit Morgoth (see below) gets up to to which his responses are either because of restrictions placed on him or because he is a lazy useless moron, apparently being so good that he literally doesn't comprehend things like deception. Debate continues.
• Varda, Queen of the Valar and creator of the stars. Married to Manwë. Varda is more commonly known by her Sindarin name, Elbereth, and is revered among the elves as the bringer of Light, and by extension, the defeat of Darkness. Out of all the Valar, Morgoth hates her the most because she was the first to realize his own innate evil and the fact that he is her complete opposite in every way. Elves (and hobbits like Frodo) invoke her name when confronted with evil, which can unsettle their opponents.
• Aulë, The Smith. Married to Yavanna, and creator of the Dwarves (though he could only create their form, Ilúvatar later gave them life and free will of their own). Both of his best disciples went traitor (Sauron and Saruman). The Noldor elves also considered themselves students of Aulë, though like Sauron and Saruman, Fëanor fell to evil as a result of Morgoth turning the Noldor elves against the Valar. Aulë and his student's power to create makes them the most powerful of the Ainur, but that power can lead to evil if they're consumed by pride and a desire to control, which is why some of them turned traitor in the first place.
• Yavanna, Giver of Fruits. Married to Aulë. Besides her domain being nature, she also created the Ents to protect the trees from over-foresting dwarves. If the Valar were depicted as Dilbert characters, Yavanna would definitely be Alice.
• Mandos, Ruler of the Dead, and the Doomsman. All dead elves and men arrive in his halls, whereafter they go to their separate fates. He is also the judge of the Valar, presiding over Melkor's trial and pronouncing the Doom of those who transgress the Valar. Married to Vairë. His real name is actually Námo. Cryptic, in a "not sure if grimdark or troll" kind of way.
• Vairë, the Weaver. Married to Mandos, and records all of history on her ever-growing tapestry.
• Oromë, the Huntsman and Lord of the Forests. He was the first to discover the elves and invite them to live with the Valar in Valinor. Married to Vana.
• Vana, the Queen of Flowers, married to Oromë. Vana is Yavanna's sister but of the two Yavanna is unquestionably the senior in ability and power.
• Irmo, Master of Dreams, married to Estë. He would give prophetic dreams and visions to mortals in need. Together with his brother Mandos he is one of the Masters of the Souls.
• Estë, Lady of Rest & Healing. Elves who visit her and her husband's domain can recover from their weariness.
• Tulkas, Champion of the Valar, married to Nessa. He was the last to arrive in Arda, and was one of the few powerful enough to challenge Melkor at the height of his power, wrestling and imprisoning him with his own hands. Total gym-bro.
• Nessa, the Dancer, married to Tulkas. She's Orome's sister and shares his love of the wilds, but doesn't really do anything and is regarded (even by the Valar) as the least of the Valar.
• Ulmo, Lord of the seas, and the most proactive ally to the free peoples. One of the few to not trust Melkor in the beginning. As his home is not in Valinor but in the seas, he's the one who interacts the most with mortals. Comes off as really intense.
• Nienna, Lady of Mercy, Grief and Compassion. She had been Gandalf's instructor, which allowed him to empathise with the free peoples, in particular the hobbits. Alongside Irmo and Ulmo, she's definitely among the most competent of the bunch (the rest being either useless swanabouts or obsessive compulsives), given she was Gandalf's master and Gandalf basically carried the entire fight against Sauron on his back.

Of similar power but opposed to the Valar, is Melkor, aka Morgoth, the first Dark Lord and enemy of the Valar. Originally he was the most powerful of all the Ainur, but back during the music of the Ainur, he had become bitter and jealous that he could not create life on his own, and began rebelling against Eru Ilúvatar. Thereafter, he kept trying to dominate Arda to his will, corrupting it with his power and making war with the Children of Ilúvatar. Eventually, he'd spent enough of his power that he was captured and imprisoned by the Valar, only to be released when they thought he had been reformed. This was a ruse, and he continued to conquer Middle Earth throughout the first age, even causing the Noldor elves to rebel against the Valar just to get revenge on him. Melkor was finally defeated when the elves pleaded with the Valar to rescue them, causing him to be imprisoned beyond the boundaries of Arda until the end of time. Despite this, Morgoth's influence lingers as Sauron had set up cults to Morgoth, which had been especially prevalent at the end of the Second Age. Supposedly Morgoth will re-emerge at the end of the world when the Door of Night is destroyed, leading to the Dagor Dagorath, ending in his final defeat. Supposedly Eru will give Turin Turambar the honor of finishing him off as reward for putting up with all the shit Morgoth put him through.

Maiar

The lesser Maiar take many different forms throughout the series, though many served under each of the Valar at some point. In comparison to the Archangel-like Valar, Maiar are generally equivalent to lesser angels.

• Gandalf, Saruman, Radaghast, Rámostamó & Morinehtar : See Below.
• Eönwë: He is the banner-bearer and herald of Manwë, and shares the chiefdom of the Maiar along with Ilmarë. Eönwë was sent to Middle-Earth, at the end of the 1st Age, to lead the Host of the West against Morgoth, and it is said that it was he that overthrew that Ainu. After the War of Wrath, he went among the Númenóreans and, with the authority of the Powers and Eru, blessed that people with longer lifespan, taught them crafts and lore and brought flora and fauna from Valinor (including a seedling of the White Tree). It is prophesied that, when Morgoth returns to destroy Arda, Eönwë and Túrin Turambar will slay him forever.
• Ilmarë: She is the handmaiden of Varda and, as said before, a chief of the Maiar. Unlike Melian, she remain in Valinor in content and nothing more is known about her.
• Melian: Noteworthy for being the progenitor of both the Half-Elves and the Kings of Gondor, she married the Elven king of Doriath and bore Lúthien, who would herself marry a human named Beren. As this shows, it was possible for Maiar in their physical forms to procreate with the Children of Ilúvatar, which has some interesting implications (and potentially disturbing ones, see 'Boldogs' below). She protected Doriath with her magic until her husband was killed by a bunch of angry Dwarves, and eventually returned to Valinor heartbroken.
• Sauron: Most powerful of the Maiar. Formerly a student of Aulë but later was swayed to Morgoth's side. He is ever so slightly less of a dick than Morgoth, which still left a lot of room for satanic-tier dickishness. While Morgoth wanted to destroy the world and recreate it from scratch in his image, Sauron wanted to Dominate it and shape its peoples and societies into his own "idealized" (read:hellish) image. Whereas Morgoth was more motivated by jealousy and vengeance against Iluvatar and the Valar, and used brute strength to impose his will, Sauron was motivated by a desire for order, and favoured guile and manipulation, especially when he successfully corrupted the kingdom of Númenor and brought about its ruin, or when he used his Ring to dominate the wills of others. He's taken on other guises as well; such as "Annatar the Lord of Gifts" to deceive the Elves of the Second Age, or the Necromancer of Dol Guldur when he was in hiding. Sauron poured practically all of his power into his ring, which not only prevented his power from fading (as it did with Morgoth), but also allowed him to survive his initial disembodiment until the War of the Ring, when the destruction of it robbed him of all his power and reduced him to an angry and completely-powerless ghost floating through space.
• Balrogs: Balrogs are greater Maiar who sided with Morgoth and took the form of fiery demons. The one in the Fellowship of the Ring, Durin's Bane, is one of the last remaining ones; Morgoth used to field armies of these guys.
  • Gothmog: Lord of the Balrogs, killed in the Fall of Gondolin when Ecthelion of the Fountain charged him and they both drowned in the gigantic pools of the city.
    • In the Third Age, an Orc/Black Númenórean/SOMETHING adopted Gothmog's name for themselves and served as the lieutenant of Minas Morgul and second-in-command to the Witch-king. They were present at the Siege of Minas Tirith, but their fate after that is completely unknown. Aside from this, nothing is known about them. In the movies, Gothmog was portrayed as a Orc General with a hideously misshapen face and tumor-like deformities all along the left side of his body.
• Boldogs/"Orc-shaped Maiar": Lesser Maiar who were seduced to Morgoth's side, but instead of taking the shapes of fiery demons like the Balrogs, they took the forms of Orcs. Although less powerful than the Balrogs, these creatures were still powerful and were usually in command of Morgoth's many armies. Earlier versions of Tolkien's legendarium did not have a name for these types of creatures, and Boldog was instead the name of an Orc Chieftain killed by Thingol. Later versions removed this character and suggested in a footnote that instead it was a title or species-type for "Orc-formed Maiar", which suggests that Tolkien never got around to finalising this concept alongside the exact origin and nature of Orcs. Their presence within the lore however, could have been the set-up for one of Tolkien's many abandoned attempts at explaining the origins and evil nature of Orcs, for making them the rape-spawn of these aforementioned fantasy Fallen Angels would certainly explain just why the Orcs are so demonically twisted in both flesh and spirit; but like the many other attempts at an answer for the Orcish question, the good professor likely abandoned the idea early on due to the many uncomfortable implications of the idea and questions of faith it brought up within himself regarding how someone can possibly be born already predestined to be evil.
• Arien & Tilion: these two became the bearers of the Sun and Moon, which were the last fruit & flower of the Two Trees of Light that Morgoth killed. Arien was one of the fire spirits that Morgoth couldn’t sway to his service, and she is said to be the second most powerful Maiar. Tilion is not as powerful, and more reckless, resulting in the phases of the moon and eclipses. He is said to be the Man in the Moon and Arien’s lover.

Istari

The Istari is the formal name of the Wizards, all of whom were Maiar who were sent to Middle Earth to aid the free peoples and provide them with wise counsel during the Third Age between Sauron's initial defeat and his final one. Though they appear to take the form of elderly men, they're still quite powerful in their own right, both physically and magically. Compared to the other Ainur on this list, the Istari have a fully embodied experience while in Middle Earth; meaning that they have fully physical bodies capable of hunger, weariness and death, making them more vulnerable to both physical harm and corruption, but also better able to interact with the people of Middle Earth. There are five of them in total. In order of power and rank they are Curumo (Saruman), Aiwendil (Radagast), Alatar/Morinehtar and Pallando/Rómestámo (the Blue Wizards), and lastly Olórin (Gandalf). The important thing to understand about the Istari is that they are not spellcasters or conjurers; their magic is an inherent part of their nature as Maiar, and we get a glimpse of that when Gandalf drives away the Nazgul with what looks like a blinding light coming directly from his body.

They were sent by Manwë to inform mortals about Morgoth's lieutenant Sauron and raise forces amongst the Free Peoples to oppose him, they were however restricted from directly leading them or otherwise doing all the fighting, as there was the (justified in hindsight) fear that they could fall just like Sauron did and desire to dominate and rule Middle Earth instead of liberating it. The Istari also do not use their real names, instead using names given to them by the peoples of Middle Earth. While the Istari are all immortal beings from Valinor, their memories of that land become dimmed upon reaching Middle Earth; if they abandon their mission, they forget nearly all of it. Readers only learn to what happened to three of them.

Saruman the White: was corrupted after learning about the nature of the rings of power and its ruling ring, and fell completely after gazing into the Palantir of Orthanc and being subdued by Sauron. Saruman coveted the One Ring and desired to find and take it for himself, and being a Maiar of the same level as Sauron, could have theoretically been able to successfully exploit the One Ring and claim its power for himself, thus becoming a new Dark Lord. Even before the hunt for the One Ring, Saruman was vulnerable to corruption, as he was prideful and jealous that Gandalf had been proposed as leader of the White Council, and resentful that Yavanna had begged him to take Radaghast with him to Middle Earth; that being said, he did not initially plan on doing anything evil until he became obsessed with the Ring. At some point, Saruman casts aside his title of 'the White' in favour of becoming Saruman of Many Colours as a show of dominance and mastery. Saruman's treason and ultimate defeat is of course the first half of the plot of the whole series. The nature of his death and defeat differs between the books and film. In the films he perishes during the final confrontation at the Orthanc, being stabbed in the back by a vengeful Grima Wormtongue. In the books he survives until the very end of the story, where he tries to take a petty revenge upon the hobbits of the Shire by taking it over with a bunch of criminals and... industrialising it. That's right, Saruman's retirement plan was to become Big Tobacco. The Hobbits overthrow his mafia-regime, and after abusing Grima Wormtongue one final time, gets his throat slit by the fed-up lackey.

Some time before (or after, if you're a film scrub) the events of the Hobbit, Radagast the Brown: lost sight of his purpose as a Wizard of the order, and instead became infatuated with Nature and its wild animals, likely falling to his own inborn callings and affinities as a Maia of Yavanna, the Vala of Nature. Despite losing track of his true mission, Radagast never completely abandoned it, and still served as a messenger for Saruman and did train birds to assist both Saruman and Gandalf, even if in those purposes he served as a cat's paw for the traitorous Saruman. It could also be said that by focusing on the natural world, Radagast still aided the Free Peoples by defending Nature against the industrial depredations of The Enemy.

Gandalf the Grey: was the most proactive, counselling Elves, Dwarves and men. Despite not being the leader of the Istari, the elves perceived Gandalf's wisdom on their first meeting, and initially wanted him to lead the White Council. Ever since his arrival, Gandalf worked tirelessly to council and rally the free peoples and give them hope against the evils that lingered during the Watchful Peace. He was responsible for the events of The Hobbit, which saw the northern Orc armies and Smaug, the last dragon of any real strength, dead. He initially led the Fellowship until he was pulled down to the bottom of dwarf mines of Khazad-dûm by the Balrog, Durin's Bane. Fought and chased the bastard up the Endless Stair for days, and died after killing it, with the duel itself destroying Durin's Tower at the top of the peak. He was then upgraded to Gandalf the White by Eru Ilúvatar, where he was given Saruman's authority and loaned an extra dose of power, and was given a ride back to the action by the Eagle Gwaihir the Windlord (the lord of the Giant Eagles), thus rejoining the Fellowship. He fucked off to the Undying Lands after the War of the Ring as retirement is the only thing you can do after the defeat of the BBEG. Also had some pretty cool gear with him, such as his sword Glamdring, the Elven Ring of Fire: Narya, and a Wizard Staff he often dual-wielded with Glamdring. The latter being upgraded when he became the White Wizard in the place of Saruman.

As for the two Blue Wizards:, we're only given scraps of speculative information. All we know for sure is that they headed East and South into the lands where Sauron held sway. One version says that they ultimately failed in their mission or even became wayward, possibly creating cults of magic. Another, however, says that they were successful in creating uprisings and occupying the vast forces of the East and South, preventing those forces from coming to the aid of Sauron in the War of the Ring. Regardless of whether the Blues succeeded or failed, they and Radagast likely returned to Aman as well.

Other

• Tom Bombadil: Exists specifically to fuck up neat and tidy classification systems. (Distant sound of Professor Tolkien's Ghost laughing).
• Ungoliant: Her exact nature is unclear, save for the cryptic note that she existed before Arda and came into it early on, which implies a lot. The mother of Shelob the giant spider, Ungoliant herself was an even more massive spider monster who was the progenitor of all other giant spiders in the world. Not that she was a good mother, she only gave birth to other spiders to have something to eat and studs to breed new spiderlings with before devouring. Her ultimate drive was an insatiable hunger and a contempt for everything else that lived. Ungoliant hated the light but also gained power from consuming it, so she temporarily allied with Morgoth to destroy the Two Trees of Light. When their alliance was dissolved, she nearly killed Morgoth for trying to hide the Silmarils from her, but was driven away by the Balrogs that Morgoth screamed for to save him. She eventually became so hungry that she ate herself.