I have studied calculus and a bit of linear algebra. And now, I'm finding a book about analysis, which I can self-study. Can anyone recommend me a good analysis book which has many examples, and is compact?
You should definitely try T.Tao's Real Analysis I then Analysis II. It consists of nice exercises and the terminologies are quite simple, and he also gives Remarks at the end of propositions or Theorems which might be a bit too rigorous for new readers to understand fully and thus clears ambiguities.
There's Baby Rudin too, but i would not recommedd it as the first book though, it can be read later after Tao's book