In this book we discuss the problems entitled "Fixed point and Common Fixed Point Theorems in Metric Spaces". The work follows many different previous results and obtains some new results. The present work reported in the book has been organized into eight chapters and covered a wide area of metric space and other concerning space like, L- space, Banach space, G- Banach space, and proved some fixed point and common fixed point theorems in this spaces. The first chapter deals with introduction which contains a detailed presentation of fixed point theorems. It also contains the recent investigated concepts which have played key role in the investigations which are proved in consequent chapters.