Synchronization phenomena in population of interacting elements are the subject of intense research efforts in physics, chemistry, biology and social scince. Here, the synchronization phenomena are introduced, then the Kuramoto model is designed. One of the interesting questions in the Kuramoto model is the stability of solutions, both synchronized and incoherent states. In this thesis, by a synchronized state we mean a state in wich all to of the oscillators oscillate with the same frequency this is also called a frequency locked state. The aim of this thesis is investigating the role of topology and properties of networks such as Erdos Renyi network, scale free network with Barabasi Albert model and the so-called Achlioptas networks on synchronization. The Kuramoto model is applied on all-to-all networks with unimodal and bimodal frequency distributions. The diagram of order parameter as a function of time is drawn for synchronized state and the threshold of synchronization. Furthermore, this diagram shows that when coupling constant (k) is less than a threshold value, the system is not synchronize and by increasing coupling constant, the system reached to the synchronization threshold, if coupling constant is more than threshold value. Bipartite networks are introduced and the Kuramoto model is studied for these networks with bimodal frequency distribution. Time evaluation of order parameter is drawn for synchronized and asynchronized modes. While coupling constant is less than threshold, the system is asynchronized and by increasing coupling costant, the system will inter to synchronization. Finally, the scale-free and random networks are introduce and time evaluation of order parameter are compared in two networks. When evaluation the diagram is compare for scale-free and random networks, it will be found that the scale-free network reaches sooner than random network to synchronization. The Growth Achlioptas process is introduced.First define an Achliptas growth process. Here instead, the criterion to add links is different. The random and scale-free networks and designed with Growth Achlioptas process, and the Kuramoto model are applied on these two networks. Furthermore, diagram order parameter depending on the time are drawn and compared to scale-free and random networks that was made with Growth Achlioptas process.Links between nodes are introduce in order to produce a scale-free and random graph with given exponent ? for the degree distribution. For the scale-free and random networks that are made by Achlioptas method, it is found that the scale-free networks reach sooner than random network to synchronization. Key words: Network, Synchronization, Unimodal frequency distribution, Bimodal frequency distribution, Grow Achlioptas