I really like Pinter's exposition of Algebra. He breaks down each and every term and goes to extent of explaining you instead of throwing the proofs at you. This textbook is wonderful if you are a complete novice. He teaches through the exercises in the text. This is an ideal textbook for self learning.
However, I was wondering if there were any such texts on Analysis. I tried learning from Abbott's Understanding Analysis. However, he leaves most of proofs to the reader with a little to no hint.