Fixed point theory is an important and useful tool for different branches of mathematical analysis. Also, it may be discussed an essential subject of nonlinear analysis. Accordingly, in recent years many good articles and perfect surveys have regulated about fixed point theory and its application by other researcher. With this interpretation, the main objective of this monograph is to review and compare fixed point results in various spaces. For this, we consider fixed point theory and new subjects in this field for different spaces such as metric and type metric spaces, cone metric and cone metric type spaces, G-metric space, topological vector cone metric space, metric-like and partial metric spaces.