This book gives a systematic introduction of a course in Metric Spaces. An elementary book on the topic was always required which would be written in an easy language but fulfill the gap between the idea of school level and higher mathematics. The book has been written using the teaching experience of the author in under graduate level for more than a decade.Key Features:- The elementary concept of open ball and open sets are used to develop all the idea in this book- Geometric interpretations with illustrative pictures are provided in many problems- Numerous problems in meaningful context are discussed- Prepares a background for the study of Topology, Measure Theory and Functional Analysis- Lots of concrete examples of spaces and maps are provided