This book aims to make the reader acquainted with the fundamental ideas of Functional Analysis avoiding unnecessary abstractions. Indeed, much more than is commonly realized can be done in this vein. As a case in point, all what is used of topology is some elementary theory of metric spaces (developed in the book itself). Admittedly, the approach of the authors limits the generality of the results. This limitation, however, turns out to be of little importance for practical applications. Globally speaking, this book covers normed vector spaces, Banach spaces and Hilbert spaces (without going into topological vector spaces or Banach algebras). Integration theory is treated in an appendix. There is an ample collection of exercises.