In this thesis we first introduce dynamical systems. Dynamical systems fall into two categories of continuous-time and discrete-time systems. Continuous-time systems are described by differential equations and discrete-time systems are described by maps. In some cases it is impossible to obtain an analytical solution to the equations describing the systems showing a complex behavior. Chaotic systems and logistic maps which are discrete-time systems are considered. Lyapunov exponents are used as a tool to study chaos in various systems. Synchronization may occur not only in periodic oscillators, but also in chaotic oscillators, and in maps which have non-periodic and unpredictable dynamics which are sensitive to the initial conditions. Different types of synchronization and stabilities of synchronous state are described. Complex networks along with four categories of networks including regular, small world, scale-free, and random, are described, and synchronization of networks are investigated for some logistic maps. Furthermore stability of synchronous state, was studied using master stability function method and matrix measure method. Initially the coupling function is defined as the difference between two logistic maps, and in the general case coupling function is defined as the difference between two arbitrary functions, and different choices for coupling function are examined. Investigations are carried out using Matlab software. In matrix measure method, the dependence of stability on logistic map parameters, number of nodes and different network parameters are investigated