I wouldn't recommend Rudin for a first exposure to Analysis. You will undoubtably suffer unfairly if you look at Rudin and aren't in the context of a classroom

I wouldn't recommend Rudin for a first exposure to Analysis. You will undoubtably suffer unfairly if you look at Rudin and aren't in the context of a classroom and/or you lack the mentorship to have your proofs checked. It's one of those books highly recommended but unuseful for the absolute beginner. I heard better things about Spivak for the newbie. But I would Terrance Tao's notes on analysis: http://www.math.ucla.edu/%7Etao/resource/general/131ah.1.03w/ http://www.math.ucla.edu/%7Etao/resource/general/131ah.1.03w... Before you start with Tao go through all the calculus series on Khan academy & get an introductory book on proof writing.