This manual is the official definition of Lua 5.1. It covers Lua's syntax and semantics, the full API with C, and the standard libraries. Lua is an extension programming language designed to support general procedural programming with data description facilities. It also offers good support for object-oriented programming, functional programming, and data-driven programming. Lua is intended to be used as a powerful, light-weight scripting language for any program that needs one. Lua is implemented as a library, and is highly portable, being written in clean C (that is, in the common subset of ANSI C and C++).
It's a good little reference manual. Everything you need to know about Lua in about 50 pages. It includes every function in the standard library and good descriptions of most of the things that lua can do as well as a full language grammar. The reference manual is required reading for anyone who reads PiL. PiL is simply incomprehensible without it.