Lord of the Rings is a great story; it deserves every bit of popularity it’s gotten. But it’s also a gate to so much more.
So you’ve read Lord of the Rings, and you want more. Maybe you want more of Tolkien's adventures; maybe you want more of his style of writing; maybe (like me) you love Middle-Earth and you want to find out exactly who Galadriel is (beyond the bit we’ve gotten in the Amazon series) and where the Elves are going and what was up with that Fëanor who might've made the Palantíri.
Good news - there's more! Lots of it!
Tolkien built up his Middle-Earth legendarium virtually throughout his life, from his first poems about the abandoned Elven city of Kôr (which would later be morphed into Tirion) written as a teenager not yet shipped off to World War One, to the last aborted redrafting of Galadriel's motivations scribbled months before his death. And as you can guess from that, he never ceased reworking things.
His flaw was in finishing stories. Even as late as 1945 - after Lord of the Rings was in final editing - Tolkien's friend C. S. Lewis (who'd dropped a reference to "Numinor" into his own That Hideous Strength) mentioned in a letter that Tolkien's work would probably remain forever unfinished. The support of Lewis and other members of the "Inklings" writing group was (by Tolkien's own admission) what pushed him to finish as much as he did; biographer Diana Glyer points out that after the Inklings broke up, for the rest of his life, Tolkien never declared anything finished enough to be published. (There's technically one exception, The Adventures of Tom Bombadil, but that small book of sixteen short poems merely accentuates her point.)
(You could say that Tolkien laughed at himself, or at least recognized his own inadequacies, in his allegorical short story “Leaf by Niggle” about a painter who wants to paint a tree but keeps redoing one single leaf. In the story, Niggle finally sees his tree finished in Heaven. In reality, Tolkien left all his notes in the care of his son Christopher Tolkien, who finished some of it and started publishing the rest as-is.)
So, unless you want to limit yourself to Hobbit and Lord of the Rings, this constant redrafting makes it difficult to identify one single canonical history of Arda.1 But Tolkien might not be dissatisfied with that. It's no easier to identify a single canon of ancient mythologies, and often hard to identify a single full true story of history. In fact, this depth is one of the reasons I love Tolkien's legendarium so much: it simulates the richness and multiple sometimes-contradictory sources of real history. One blogger says she fell in love with Tolkien's works because he did write detailed explorations of all the questions she had when reading Lord of the Rings. I find it gives all that and more: Tolkien pretty much always rewards new study with new depths revealed.
To the interested reader, this averts the worries that Tolkien once shared in a letter:
I am doubtful myself about the undertaking [of finishing The Silmarillion]. Part of the attraction of the L.R. [The Lord of the Rings] is, I think, due to the glimpses of a large history in the background: an attraction like that of viewing far off an unvisited island, or seeing the towers of a distant city gleaming in a sunlit mist. To go there is to destroy the magic, unless new unattainable vistas are again revealed.
— J. R. R. Tolkien, Letter #247
There are always new unattainable vistas, whether it's factoids about Numenorian dancing bears (in Nature of Middle-Earth), or the exact implications of Finrod's speculations on resurrection (in HoME X: Morgoth's Ring) for his joining Beren's quest (in Silmarillion), or even just the precise end of the Lay of Leithien (partially in HoME III: Lays of Beleriand, but abandoned unfinished).
Can other writers imitate this effect? I know many fantasy writers who've tried to imitate the "glimpses of a large history" we see in Lord of the Rings, some with more success than others. I know some who've published some amount of that history. But I don't know any other writer who's even approached Tolkien's depth of detail, because I don't know any other writer who's put in so much loving effort over so many decades. The only place I’ve found something similar is in shared universes, and even they rarely have the depths of Arda and are often more sprawling and contradictory (due to the many different hands involved).
Fortunately, Tolkien left all his huge mass of notes to his very able son Christopher Tolkien - let us praise him with great praise - who sacrificed (or redirected) his own academic career to collect and publish them.
So, if you've read Lord of the Rings and you want more... Well, first I should add: If you actually haven’t read Lord of the Rings but just watched it, the next place to go is to read the book! Peter Jackson did a decently good job of hinting at the larger story, but there’s so much that the realities of filmmaking meant he couldn’t put in, even to the extended editions.
Once you’ve read Lord of the Rings, next, read Appendix A to Return of the King. If you like that briefer style closer to a history book than the main text of Lord of the Rings, you're great to start with The Silmarillion, the first book Christopher Tolkien put together from his father's closest-to-publishable writings on the First Age of Arda.
If you don't like Appendix A so much and you want more actual story... then if you don't mind being dumped into the middle of the story, you might like starting with two of the longer stories from the First Age, The Children of Húrin and Beren and Luthien. Both of them are told in Silmarillion as one chapter each, but Tolkien had expanded them to the length of a short book each, and Christopher Tolkien eventually published them as their own books. (You'll also see The Fall of Gondolin advertised as a third volume like these; it isn't, since Tolkien never completed the story after the initial 1917 version. What you see in The Fall of Gondolin book is just selections from various drafts from Unfinished Tales and History of Middle-Earth.)
Unfortunately, if neither of these appeals to you because you just want more about hobbits - then I'm sorry. All I have to recommend to you on that score is The Hobbit itself and The Adventures of Tom Bombadil. There's nothing about Hobbits in the other tales of Arda. (They had to be there somewhere; I’m not criticizing Amazon one bit for including them in its Second-Age TV series. But they didn’t make their way into the stories.) You might also like some of Tolkien's non-Arda stories that I'll mention at the end, which have a hobbit-like feel to them.
Then, once you've read Silmarillion and want more - I recommend trying the next book Christopher Tolkien put out, Unfinished Tales. It's more disconnected. As the title says, the tales are unfinished, and some more so than others - varying from "Tuor and his Coming to Gondolin" which is very polished until it breaks off mid-scene, to "Of Galadriel and Celeborn" which is disconnected sets of contradictory snippets and outlines written over decades.
If you like Unfinished Tales, there's a lot more! Christopher Tolkien sacrificed his own career to keep on assembling and publishing his father's papers throughout his life; praise him with great praise. You can continue through all the volumes of History of Middle-Earth. And even if you didn't like Unfinished Tales, there're some gems I’ll urge you to dip into.
Here're some notes on History of Middle-Earth, whether you just want to dip in or you prefer having an idea what you're getting:
I-II. The Book of Lost Tales 1 & 2 - Contains the earliest forms of Tolkien's tales of Middle-Earth. We see the first fragmentary poetry he wrote about the Elves, his specific links between his stories and the land of England, and the tales where an Anglo-Saxon mariner named Eriol visited the island of Tol Eressea and heard from the Elves the tales of the Elder Days. These first forms are very different from the eventual Silmarillion both in tone and plot, but they have their own charm. The Valar feel much more like pagan gods; Beren is an Elf; Morgoth produces biomechanical war engines; Earendil's mission is fruitless.
III. The Lays of Beleriand - Beautiful poetry. Well worth reading for itself alone. The "Lay of Leithian" in here is one of my three favorite parts of all HoME.
IV. The Shaping of Middle-earth - Further prose development of the First Age stories, which are beginning to take a shape wending toward Silmarillion. Feel free to skip if this doesn't interest you.
V. The Lost Road and Other Writings - Numenor and the Second Age! Includes an abortive time-travel story which would've taken a father and son through the ages of history back to become Elendil and Isildur in Numenor. (Also more redrafting of the First Age stories.) This’s part of the interesting out-of-universe story where Lewis and Tolkien challenged each other to write science-fiction stories; Lewis wrote space travel and published Out of the Silent Planet; Tolkien wrote time-travel and wound up with this. In-universe, the most interesting bit is a brief mention that this version of Numenor has steamships. Feel free to skip if this doesn't interest you.
VI-VIII. The Return of the Shadow, The Treason of Isengard, The War of the Ring - The first drafts of Lord of the Rings, where we can see Tolkien's first musings and abortive attempts about the plot and characters, expansion of the plot, abandoned scenes, and repeated outlining of what's next. We see the first conceptions of Aragorn as Trotter the hobbit, the first draft of an evil Treebeard, and Aragorn returning Eowyn's love before Tolkien decides to introduce the character of Arwen instead. Read if this overview of the writing process interests you. If you've gotten thorough IV and V, it probably does - though even if you haven't, it might with Lord of the Rings rather than the First Age?
IX. Sauron Defeated - Includes a draft epilogue to Lord of the Rings, where Sam is answering myriads of questions from his kids about what happened next! Also includes "The Notion Club Papers," an incomplete story about Inklings-expies who start getting visions of Numenor. In-jokes abound. Also, more draftings of Lord of the Rings, and drafts of Akallabeth. Read "Notion Club Papers" if you love hearing more on the Inklings; most of the Epilogue's questions were moved to the Appendices - and IMO, Tolkien was wise to cut it since it doesn't fit the right tone.
X. Morgoth's Ring - Perhaps my favorite book in all the History. After Lord of the Rings, Tolkien returned to the First Age. We have a philosophical debate between Finrod and Beren's great-aunt on mortality; we have a debate of the Valar on Finwe's remarriage; we have extensive notes on people's motives (including Morgoth's and Sauron's!) which might be unclear in the narratives; we have musings on the spiritual and ethical status of orcs! Also, we have Tolkien's musings on projected redraftings of the cosmology to accord with modern science. (Also, more Silmarillion drafts.) If you like philosophical musings about Arda, definitely read this.
XI. The War of the Jewels - More Silmarillion drafts, including extensive narratives such as "The Wandering of Húrin" which weren't included in the published Silmarillion. Also, Christopher Tolkien explains and apologizes for his confused construction of the Fall of Doriath in the published Silmarillion. If you liked Silmarillion and Unfinished Tales and want more, read this even if you didn’t read the rest of History.
XII. The Peoples of Middle-earth - Contains much interesting material from Tolkien's last years, including matters of Fëanor, the Blue Wizards, and the Dwarves. Also contains the first chapter of an abandoned story set late in Aragorn's reign (which Tolkien said would've been "a mere thriller"; I agree) and another abandoned story about one of the Men of Middle-Earth meeting the Numenorian colonists. Well worth reading if you like delving through the conceptions and history of Middle-Earth.
Finally, there're two other books by other editors which extend History of Middle-Earth:
The History of The Hobbit (ed. John D. Rateliff) - Rateliff does for The Hobbit what Christopher Tolkien did in History for his father's other writings. We get the early musings which would've loosely set it in the First Age, the redrafting of the riddle-game to accord with the version in Lord of the Rings, and the abortive redrafting which would've matched the tone with Lord of the Rings. (We can take that last one as a spiritual predecessor of Jackson's movie... except Tolkien wisely aborted it.) Read if this interests you; otherwise feel free to skip.
The Nature of Middle-earth (ed. Carl F. Hostetter) - Following Christopher Tolkien's death, Hostetter compiled some further notes into one final volume, stating that everything has now been published except for some material on the Elven languages. IMO, there's one valuable essay in here: Osanwe-Kenta, on Elven telepathy. Otherwise, read only if you care about completeness.
Finally, let me briefly mention some other works of Tolkien which might also be worth reading if you enjoy Arda:
The Father Christmas Letters: Not connected to Arda; the elf Ilbareth here is clearly not the same as the Vala Elbereth. These were actual letters Tolkien wrote for his young kids.
The Fall of Arthur: Also not connected to Arda; the forest of Mirkwood somewhere in Germany is pretty clearly not the same as the one between the Great River and the Lonely Mountain.
"Smith of Wootton Major": Also not connected to Arda, but has a Hobbity tone.
“Farmer Giles of Ham”: Even more of a Hobbity tone. If you liked The Hobbit, definitely read this.
Roverandum: A kids' story technically connected to Arda in that our living toy dog at one point glimpses Valinor, with a somewhat Hobbity tone. (The toy dog was real; Tolkien made up the story after his son lost it at the beach.)
"Leaf by Niggle": As mentioned above, a charming self-depreciating allegory. This’s Tolkien’s only explicitly Christian fiction. (Finrod’s debate in HoME X: Morgoth’s Ring dances along the borderline, but IMO doesn’t quite count.)
"On Fairy-Stories," and Beowulf: The Monsters and the Critics: Two nonfiction essays giving insights into Tolkien's philosophy of story. Beowulf, I’ve heard, also revitalized scholarship of the poem.
I'm using "Arda" because it's the name of the whole world; "Middle-Earth" technically refers to just the one continent, as explained in Silmarillion.
Thanks! The only parts of the Silmarillion that I liked were The Children of Húrin and Beren and Luthien. So nice to know they are now expanded stories.
Wonderful! I skimmed toward the end of the list of recommended works, but I will be coming back to this after I read the Silmarillion!