Researchers have the natural tendency to take taste of basic results under generalized setting. Fixed point theory in functional analysis has a vast literature and has many applications in solving linear algebraic equation, differential equation, integral equation, implicit function theorem and optimization theory, etc. But this beautiful theory took a turn with the emergence of 2-metric space by a German mathematician S. Gahler. Researchers have been interested to test the existence of fixed points under some assumption in this new setting. This monograph presents the reader a brief account of this evolution in this area. Some fundamental results have been stated without proof and some new knowledge has been added with proper reasoning and proof. More or less, this monograph is an outgrowth of research on the subject during the past few decades and a great deal of the material presented here has been obtained only in recent years.