The aim and intent of this dissertation titled “SPACES OF CONTINUOUS FUNCTIONS WITH ANALYSIS IN FIXED POINT THEORY”, embodies a brief account of general function paces along with the investigation of some fixed point and common fixed point results under the supervision of Professor and Dean of sciences Dr. Muhammad Arshad Zia, International Islamic University Islamabad. The main aim of this work is to study, generalize, extend and obtain fixed point theorems in the setting of complete, compact, pseudo-compact andbmetric spaces. The work presented in this thesis has been divided into five chapters. Chapter first is introductory. In this chapter, we present basic definitions and known results without proof. In chapters, 2, 3, 4 and 5, we present generalization of fixed point theorems proved by several authors in the literature of fixed point theory.