I would like to add to the list my favorite book on Classical Functional Analysis:
Dunford, Nelson; Schwartz, Jacob T. Linear operators. Part I. General theory. With the assistance of William G. Bade and Robert G. Bartle. Reprint of the 1958 original. Wiley Classics Library. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1988. xiv+858 pp. ISBN: 0-471-60848-3
This book contains a plenty of exercises, which allow to check understanding and much more.
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