It's actually Lua with the Just-In-Time (jit) compiler and Garry's Mod libraries. It's still Lua, however just with some premade libraries. Think of Java with the Swing(Graphical Interface) library. It comes with things to make your life easier.
Take a gander at lua.org/pil, the first edition is free and online. Lua is a great language to start off with, too. It really demonstrates the basics of programming and how different statements are aspects are controlled. Also, please note that Lua is not a programming language. It is a scripting language, big difference.
I recommend taking a look at other people's work, also. It's a great way to learn. Visit Facepunch.com and look under the "Developer Discussion" and "Gamemode/Addon Releases" boards. That's where all of the Garry's Mod scripters join to talk.