For representing several real problems, we used to use the concepts of sets and functions in twentieth century. This way of representing problems is more rigid. In many circumstances the solutions using these concepts becomes meaningless. To overcome such type difficulties, at present fuzzy concept is used and tried to apply at every corner of science, technology, social science, etc. Almost all Mathematical, Engineering, Medicine, etc. concepts have been redefined using fuzzy sets. This leads us to make this book. In this monograph, we have tried to explore different type of fixed point theorems in fuzzy metric spaces.Fuzzy metric space is generalized concept of metric space. There are so many concepts of metric space remain to be generalized in fuzzy metric space. That s why, at the end of each chapter, we have suggested different type of open problems. Fixed point theorem has different application in our social sciences, biological sciences, etc. That s why, we have made an attempt to write this book.Fuzzy symmetric metric space is introduced here; because it is a challenging problem to establish the concepts of mathematical analysis without using triangular inequality.