Keeping with the free theme, Book Of Proof by Richard Hammack is a nice introduction to proofs and formalism. It's available free from the author as a PDF[1], and also as a physical book on Amazon[2].
An alternative if you're willing to spend a little is How to Prove It by Daniel J. Velleman, also available from Amazon[3] and probably many other retailers. Both books cover roughly the same topics.
An alternative if you're willing to spend a little is How to Prove It by Daniel J. Velleman, also available from Amazon[3] and probably many other retailers. Both books cover roughly the same topics.
[1]: http://www.people.vcu.edu/~rhammack/BookOfProof/
[2]: http://www.amazon.com/Book-Proof-Richard-Hammack/dp/09894721...
[3]: http://www.amazon.com/How-Prove-It-Structured-Approach/dp/05...