The first result on fixed points of mappings was obtained in 1911. At that time, L. Brouwer proved that: Every continuous mapping from a compact convex set in a finite-dimensional space into itself has at least one fixed point. In 1922, S. Banach introduced a class of contractive mappings in metric spaces and proved the famous contraction mapping principle: Each contractive mapping from a complete metric space (X, d) into itself has a unique fixed point. The birth of the Banach contraction mapping principle and its application to study the existence of solutions of differential equations marks a new development of the study of fixed point theory. After that, many mathematicians have studied to extend the Banach contraction mapping principle for classes of maps and different spaces. Expanding only contractive mappings, till 1977, was summarized and compared with 25 typical formats by B.E.Rhoades.