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I want to learn about congruence classes and need a book recommendation. With a lot of examples.

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I have yet to encounter anything I consider to be a "good book" on it, but you can better your search by calling it "modular arithmetic" –  andybenji Dec 15 '12 at 10:21
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You might have more luck looking for "equivalence relation" rather than "congruence classes", unless you are mainly interested in arithmetic modulo a number. –  Pot Dec 15 '12 at 10:30
    
I found this pdf that seems to be good. (Didn't have time to read it, but it seems very example heavy with examples such as divisibility rules and an application to the RSA algorithm.) Honestly, though, if this is something that interests you, you should pick up an abstract algebra book -- all this is a specific example of a "Quotient Ring", and you may find it interesting. math.uconn.edu/~kconrad/blurbs/ugradnumthy/modarith.pdf –  andybenji Dec 15 '12 at 10:33
    
@andybenji, the pdf looks promising. And I have an abstract algebra book on the way. I don't know if it covers this because I ordered it for another reason. –  Fred Kline Dec 15 '12 at 10:52
    
It absolutely should cover this stuff. Which book is it? –  andybenji Dec 15 '12 at 11:10
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My view is totally based on my experience:

I would recommend David Burton's number theory book. Though the book does not have much examples but ( like 4 or 5 (at most) on each type) but the concepts have been written in such an easy language that you may not need more examples and can directly jump to problems.

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I ordered this book. Thanks. –  Fred Kline Dec 17 '12 at 0:07
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A Pathway Into Number Theory is a good book for self-learning with lots of examples.

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I ordered this book. Thanks. –  Fred Kline Dec 17 '12 at 0:07
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Elementary Number Theory and its Applications, 6th ed., published by Pearson would be a valuable reference and resource for you!

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