Unity API or more?

Hello, I;m tying to get familiar with Unity API classes, methods, and I was wondering if that Library is the one there is.
What is Mono and MSDN and .NET framework. Are they extended libraries? Are they cross-platform?

Also, is there a book (not online) tutorial to learn the whole Unity API?

the very best way to learn unity is by doing tutorials. And MSDN is very helpful. My advice is to use c#. Some good tutorials:

http://cgcookie.com/unity/
And a very great series from peter (bergzerg?)

right now the site seems to be down, but you can find the 272!!! parts of his Hack’n Slash tutorial on youtube, here part 1:
http://www.youtube.com/watch?v=YYqzz1dy3Ak