Here's the full manual including:
- the language refenrence
- all standard library functions
- the C API.
TOC: http://www.lua.org/manual/5.1/Manual: http://www.lua.org/manual/5.1/manual.html
It's very terse. The "Programming in Lua" book, by one of the authors of the language is far more friendly (an excellent book actually, the first version is available online for free: http://www.lua.org/pil/).