I am looking for a book that teaches proofs and the book has many exercises from very simple to more difficult? I have noticed with most math books, they seem to leave out pieces too soon before the reader gets a chance to work through lots of examples of a specific level before progressing to the next level. I want more structured approach so that after a couple dozen proofs of class "A", I want to advance to class "B". I cannot overemphasize my need for exercises. BTW, this is in preparation for an analysis course.
Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand, Polimeni, and Zhang. (link below)
The nice thing about this book is that it teaches proofs from the ground up. You learn basic proof techniques in a variety of mathematical areas including analysis, abstract algebra, and number theory. The book is very simple to read and has lots of great exercises, including very easy ones as well as more challenging ones. It presupposes no background in any of the aforementioned fields.
The nice thing is that you can get a taste of the different kinds of mathematical proofs (including the $\epsilon-\delta$ proofs you'll be seeing a lot of in analysis) in a simple, clear, informative setting. I.e., the things that you learn to prove and are proved for you are not that advanced, but the help illuminate what really goes on in a proof.
The link I put is to the 3rd edition, but I see that the 2nd edition is available on amazon at a much more reasonable price.