Multiplex and Multilayer Networks is a collection of some of the results obtained in the new field of complex networks theory with respect to multilevel, multiplex, and interacting networks. The ever-increasing availability of data in fields ranging from computer science to urban systems, medicine, economics, and finance shows that networks that were usually perceived as distinct and isolated are, in reality, interacting with other networks. While this sounds like a trivial observation, the interactions in multilevel complex networks can lead to unexpected behaviors and allow systemic vulnerabilities to emerge. The research activities of many different laboratories and groups in this field have been financed by the EU MULTIPLEX project (http://www.multiplexproject.eu). This project utilized 23 distinct research teams across Europe and, from 2012 to 2016, explored this new area of research. The results, presented in this volume, range from the theory of static multinetworks to dynamical process on them, to their percolating properties, and, finally, to applications in the case of social systems.