This book discusses the synchronisation in complex networks. At first, the basic concepts of complex networks, including the description of the network, the degree of the node, clustering coefficient, and the average path length are introduced. When the initial states of nodes are near enough to synchronisation manifold, the master stability function method is applied to analyse its local stability. However, when the initial states of nodes are randomly distributed, the Lyapunov function method is used to analyse the global stability of synchronisation manifold. Furthermore, the connection graph stability method is used to investigate the global stability of synchronisation in complex networks with time-varying network topology.