Now revised and up-dated, this brisk introduction to functional analysis is intended for advanced undergraduate students, typically final year, who have had some background in real analysis. The author's aim is not just to cover the standard material in a standard way, but to present results of applications in contemporary mathematics and to show the relevance of functional analysis to other areas.

Unusual topics covered include the geometry of finite-dimensional spaces, invariant sub-spaces, fixed-point theorems, and the BishopPhelps theorem. An outstanding feature is the large number of exercises, some straightforward, some challenging, none uninteresting.