All of the PC races in the PHB are available, however Elves and Gnomes are slightly altered.
Additional Player Character races: Kobold, Tabaxi.
Other races are subject to DM approval.
NOTE: Players should never feel constrained by the typecasting of demi-Human races, but they should be the exceptions to the general rule that NPC demi-Humans behave according to type. True diversity belongs to Humans.
Dragonborn
Dwarf
Elf
Gnome
Half-Elf
Half-Orc
Human
Kobold
Tabaxi
Tiefling
Once again, Player Characters should never feel constrained to play to type, but NPCs will almost always conform to the types described.