What are some math books that cover sets, relations...? What are some math books that cover the following topics,


*

*Sets & Relations

*Matrix

*Permutations and Combinations

*Basic Counting principles

*Probability Theory

 A: Kenneth Rosen's Discrete Math with Applications would covers pretty much everything, save for matrices.  Edit: I take that back; Rosen's Text does cover matrices, but just the basics.  For an overview, Table of Contents, and text related resources, see: Rosen, Discrete Math. 
As far as understanding matrices, the obvious topic that comes to mind would be some intro text in linear algebra, but I'm sure you could find some on-line tutorials on matrices that would satisfy your needs, for that topic. 
In addition to the text above, a great resource, IMO, is (free of charge) The Khan Academy, a tutorial-like website that provides 12 minute lectures in a whole host of topics (under linear algebra, e.g., the video tutorials start with matrices, and under probability, you can find video tutorials on combinations, permutations, counting, etc.). In addition, there are exercises corresponding to the lessons, and I believe you get immediate feedback as to your level of understanding. It's designed to be self-paced.
(If you visit the site linked above (Khan Academy), be sure to scroll up and down the page to get an idea of all the subjects covered there!)
A: Schaum's Outline of Probability covers everything on your list. The treatment of matrices though is fairly superficial so if you want more depth there you will need to look elsewhere, say, Schaum's Outline of Linear Algebra, by the same author.
