As you probably know by now, LÖVE is a framework for making 2D games in the Lua programming language. LÖVE is totally free, and can be used in anything from friendly open-source hobby projects, to evil, closed-source commercial ones.
This reference manual contains the full Lua API for each LÖVE module. You'll find an overview of the modules on the page about love.
Never used Lua before? It's a really cool language! This manual won't teach you Lua, but fortunately there are other good resources for that.
This is the full source for 'hello world' in LÖVE. Running this code will cause an 800 by 600 window to appear, and display white text on a black background.
function love.draw() love.graphics.print('Hello World!', 400, 300) end