Functional Analysis:

Chapter 5 of Folland's Real Analysis and/or chapters 1-3 of Conway's A Course in Functional Analysis are a good place to start -- as are chapters 9 and 10 of Royden's Real Analysis and chapters 0,1 and 3 of Robert J. Zimmer's Elements of Functional Analysis. For more adventure, chapters 4 and 5 of Rudin's Real & Complex Analysis and chapters 1-3 of Pedersen's Analysis Now are sophisticated, but excellent resources.