In this book we explore networks of many-body quantum systems, seeking to describe the new quantum and topological phases that arise from the interaction of individual sites. Tested networks are based on the semi-classical Lipkin¿Meshkov¿Glick model, and the couplings between different sites of the network are described with either one or two coupling constants. The effect of introducing a second coupling was studied on the example of a one-dimensional chain ¿ an extension of the SüSchrieffer¿Heeger model to the many-body systems ¿, where the interplay between topological and quantum phases was the main question.