The 5e information on the planes is, at the time of writing, sparse. There’s some in Dungeon Master’s Guide, but only broad strokes. Mordenkainen’s Tome of Foes alludes to some more details when discussing some extraplanar creatures. Sword Coast Adventure Guide and Eberron: Rising from the Last War discuss some of the cosmology of the Forgotten Realms and Eberron, respectively. But ultimately, there is effectively not much.
Planescape
Previous editions are much, much more detail-rich about the planes. The wider multiverse was, itself, a detailed campaign setting known as Planescape.
Second Edition
Second edition is where the vast, vast majority of Planescape material can be found. Also, whereas 3e tends to avoid making assumptions about other books someone might own, and thus does not really go into planar concerns outside of specific books dedicated to them, in 2e they tended to assume every book was in play and so planar concerns might crop up anywhere and everywhere. This makes providing a list prohibitive.
However, there is a book literally entitled Inner Planes—that is, the elemental ones. That one should definitely be worth a read for you.
Anyway, to offer a bit more detail, 2e introduced the “Great Wheel” as the explanation of the planes, which 5e has restored to its rightful place. The Great Wheel refers to the “Outer Planes,” sixteen aligned planes around the neutral plane known as the Outlands. These are arrayed much like your typical alignment grid, with Lawful-Good Mount Celestia in the “upper left” and the Chaotic-Evil Abyss in the “lower right.” As typically presented, the top part of the wheel is Good (the “Upper Planes”) while the bottom part is Evil (the “Lower Planes”), and the left side is Lawful while the right side is Chaotic. (Of course, since it’s a ring, these designations are fairly arbitrary.) Within the wheel were the Inner Planes (of elements and energy), and within those was the Material Plane (where the vast majority of other campaign settings can be found).
Aside from the planes themselves, major points of interest in the Great Wheel include Sigil, which is the great City of Doors atop the infinite Spire in the middle of the Outlands, and is considered the exact center of the multiverse (about which the “wheel” revolves). Sigil is ruled by the enigmatic Lady of Pain, who enforces very few rules but among them is that she is not to be worshiped as a goddess; violations of this rule are punishable by flaying, a punishment which the Lady delivers personally. Another rule is a bar on gods and other so-called “powers”—the Lady summarily curb-stomped the last one who challenged that rule, and the complete and utter lack of any attempt by others to challenge it suggests she could do so again.
The other notable thing are the exemplars, the creatures of raw belief and alignment that spawn naturally on the Outer Planes. They are (left-to-right, top-to-bottom) the LG archons, the NG guardinals, the CG eladrin, the LN modrons, the N rilmani, the CN slaad, the LE devils, the NE yugoloths, and the CE demons. I’ve written more about the exemplars here.
Third Edition
Third edition, or more specifically “v.3.5 revised edition,” had two dedicated Planescape books, Manual of the Planes and Planar Handbook. Other books such as Fiendish Codex I and II, Lords of Madness, and Fiend Folio also touch on the planes to a fair degree.
Third edition expanded upon 2e’s Planescape, but for the most part it just translated various 2e things into 3e terms. There is novel stuff in there (particularly in the Fiendish Codexes), but 2e is still the primary source.
Fourth Edition
Fourth edition had a number of unexplained, and unpopular, departures from the canon of prior editions, and 5e has seemed to be quietly ignoring a lot of them. Nonetheless, this is where you would look for various planar features that originated in 4e (its novel content tended to be more popular than its alterations to existing content), like the Feywild. Like 2e, 4e explicitly assumes all books are “core,” which does again tend to cause things to be a bit scattered all over the place.
Also, 4e just didn’t do a lot of fluff—where 2e and 3e included books with hundreds of pages of near-solely fluff, going into the setting in great detail, 4e tended to limit fluff to a sentence or three in the introduction to some mechanical option (whether it be a class, a feat, or a monster). So there just isn’t as much to find in 4e anyway.
You are probably safe ignoring 4e unless you are particularly interested in the Feywild or the Elemental Chaos (and much of the detail of the latter seems to have changed in 5e, since we have the elemental planes again that 4e replaced with the Elemental Chaos).
