I'm self-teaching math at home. After learning Calculus by MIT OCW and a bit of easy Linear Algebra and set theory, I have decided to study Analysis.
As many have recommended Baby Rudin, I've tried to study Analysis with it. But it was so tough and hard that I could only solve 1 or 2 problems on the exerices. I thought that this is not the book which I can deal with. So I look around another books.
Here's a list: Tao's Lecture Notes(Solution available and it seems to be approachable) #Since I'm studying only by myself, so Solution availabiltiy is somewhat important as I should check my answers and be given some feedback. Marsden(I didn't carefully read the contents, so I don't know what the level of this book is. But I've heard after some chapter , it has lots of errors.) Abbott(it looks like the easiest one I've seen among Analysis books) Apostol(It deals with a lot of stuff, which I'd like to know. But the exercises looks difficult for me.)
Which book should I use? If I choose a book and after studying the book, should I study harder Analysis book like Rudin?