A whole host of Dungeons & Dragons source books are available from Wizards of the Coast, ranging from Monster Manuals, to Dungeon Master’s Guides to complete Adventure Campaigns.
As a player, your wallet can breathe a sigh of relief as the majority of these books will not be relevant to you; only the books with rules pertaining to your character are required.
D&D Basic Rules
The Basic Rules are available to download for free from Wizards of the Coast (WotC). The Basic Rules include instructions to play as a Cleric, Fighter, Rogue or Wizard and also includes a selection of spells, backgrounds and races. More than enough to get a player started.
They can be found for download here.
The Player’s Handbook
The Player’s Handbook (or PHB) is considered one of the three Core Rulebooks for D&D, alongside the Dungeon Master’s Guide (DMG) and the Monster Manual (MM). Every player should have a copy of the PHB. It includes the complete rules for all of the core races and classes, combat, skills, equipment, character customisation and over 300 magic spells.
The Elemental Evil Players Companion
The Elemental Evil Player’s Companion (EE) was published by WotC to accompany the Princes of the Apocalypse adventure. It can be downloaded for free and contains rules for a number of new player races, Aarakocra, Deep Gnomes, Genasai and Goliaths, and a large selection of new elemental magic spells (Many of which were republished and refined in The Xanathar’s Guide to Everything).
It can be found for download here.
The Sword Coast Adventurers Guide
The Sword Coast Adventurers Guide (SCAG) is a campaign setting concerning the Sword Coast region of Faerun, the land in which the majority of 5th Edition D&D is set. It also includes some additional races (Duergar & Deep Gnomes) and variant sub-races for Halflings, Half-Elves and Tieflings. Also found in SCAG are a number of additional Archetypes for the core character classes found in the PHB and a handful of combat cantrips.
Volo’s Guide to Monsters
Volo’s Guide to Monsters (VGtM) is primarily a dungeon master’s resource, containing information and stat blocks on various monstrous races. It does include a number of additional player races however; Aasimar, Firbolg, Goliath, Kenku, Lizardfolk, Tabaxi, Triton and rules for playing a variety of Monstrous Adventurers.
The Xanathar’s Guide to Everything
The Xanathar’s Guide to Everything (XGtE) is probably the most popular secondary player resource as it includes dozens of additional class archetypes and 95 new magic spells.
Mordenkainen’s Tome of Foes
Mordenkainen’s Tome of Foes (MToF) is, like VGtM, primarily a DM resource including information and stat blocks for many extra-planar monsters. For players it includes some additional races; Githyanki, Githzerai, Duergar and Deep Gnomes, and a number of extra Elf and Tiefling variant sub-races.