TITLE: book recommendation on functional analysis
QUESTION [13 upvotes]: I recently started studying functional analysis. I have many ebooks loaded on my laptop, but can't figure out which one to start with. I've asked my instructor, and he says there aren't any specific books to start with. Here's a brief list of the topics on our syllabus:

Normed linear spaces
Banach Spaces
Hilbert spaces
Compact Operators
Knowledge of $C[0,1],L^p[0,1]$
Continuous linear operators
Hahn-Banach theorem   
Open mapping and Closed Graph Theorem  
Uniform Boundedness Principle

I'm seeing these topics first in my lifetime. One thing I want to ask is whether functional analysis is very difficult. Please suggest some books to start this topic which covers the above and contains some exercises. Thanks in advance.

REPLY [4 votes]: The very best introductory text on functional analysis that exists is the classic Functional Analysis by Bachman and Narici. Using a background of only basic linear algebra and advanced calculus/elementary real analysis/honors calculus, the authors develop all the standard topics on function spaces clearly and simply, with many examples and exercises. Best of all,it's available from Dover,so it's very inexpensive! To me, this is the very best self-study text that exists on the subject and I'd heartily recommend it to any beginner.