Can you recommend a gentle introduction to the abstract thinking and motivation of functional analysis? I'm looking for a book that holds you by the hand and shows the details of exercises, etc.
Of the well written books on Functional analysis that I've seen, Kreyszig is the most elementary. The Amazon reviews seem to agree with me.
Erwin Kreyszig Introductory Functional Analysis or Rynne & Youngson Linear Functional Analysis.
Both are elementary, well-written and self-contained.
I would recommend Introduction to Functional Analysis by S.C. Bose. The text is really good and simple to understand; there is a considerable number of solved exercises and examples. I'm getting a desire to re-read!