What are the best introduction books to mathematical proofs in undergraduate mathematics? I know of "Proofs from the Book" by M. Aigner and G. Ziegler, but also need one that shoots to analysis kind of proofs.
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The William Lowell Putnam Competition is an excellent example of undergraduate proofs which are fun to solve. You can buy their book or find their problems online. I'm 14 years old but I like it since it gives me a nice look at a variety of elegant proofs which helps high school proof-writing as well. I highly recommend it!
Not a book, but a nice and (very) brief intro is provided by Joel Feinstein's camcasts (these and these) and the accompanying materials. On the same site, he has also posted an introductory course on real analysis (course materials and recordings of the lectures included) where you can find further "analysis kind of proofs".