This is a vector based program, which is based on line and shape drawing, which works alongside Photoshop in Digital Imaging.
These two resources are worth having a look at, which are accessible from this site:
Youtube - the basics you need to know
and
Online: http://www.designbolts.com/2014/08/04/50-all-time-best-adobe-illustrator-tutorials-for-beginners/
As a .pdf
Illustrator for Beginners tastytuts
As well as Sydney University course notes from my training (due January).