Fixed point theory is a rich, interesting and exciting branch of mathematics. It is a relatively young but fully developed area of research. Study of the existence of fixed points falls within several domains such as functional analysis, operator theory, general topology. Fixed points and fixed point theorems have always been a major theoretical tool in fields as widely apart as topology, mathematical economics, game theory, approximation theory and initial and boundary value problems in ordinary and partial differential equations. Moreover, recently, the usefulness of this concept for applications increased enormously by the development of accurate and efficient techniques for computing fixed points, making fixed point methods a major tool in the arsenal of mathematics. The present book consists of some fixed point theorems in metric spaces(for six mappings satisfying rational inequality) , cone metric spaces, semi-metric spaces, Banach spaces and 2-Banach spaces.