The book is intended to serve as a textbook for an introductory course in functional analysis for the senior undergraduate and graduate students. It can also be useful for the senior students of applied mathematics, statistics, operations research, engineering and theoretical physics. The text starts with a chapter on Preliminaries discussing basic concepts and results which would be taken for granted later in the book. This is followed by chapters on Normed and Banach Spaces, Bounded Linear Operators, Bounded Linear Functionals, The Concept and Specific Geometry of Hilbert Spaces, Functionals and Operators on Hilbert Spaces and Introduction to Spectral Theory. An appendix have been given on Schauder Bases. The salient features of the book are presentation of the subject in a natural way, description of the concepts with justification, clear and precise exposition avoiding pendantry, various examples and counter examples, and graded problems throughout each chapter. Notes and remarks within the text enhances the utility of the book for the students.