The authors strongly believe and it is universally accepted that the basic techniques and results of topology are indispensable for the growth of most areas of pure and applied mathematics. Beginning with the preliminaries and historical notes (sets and functions and related topics), the text moves on to metric spaces, which are discussed in detail. Next, the focus shifts to topological spaces, compactness and connectedness. After that, separation axioms are taken up. Then additional matter on metric spaces have been provided. Finally, homotopy and the fundamental group have been described. Moore-smith convergence etc, have not been included since those topics are not taught in the first course. In the appendices the concept of topological vector spaces and simplicial complexes have been discussed. This book also contains adequate number of examples, counter-examples and exercises to aid students to gain experience in problem solving. The authors from their experience in teaching the course for numerous years, strongly feel that this book will be most suitable for the course.
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