Part I: Single and multilayer networks 1. Complex systems as multilayer networks Part II: Single networks 2. The structure of single networks 3. The dynamics on single networks Part III: Multilayer networks 4. Multilayer networks in nature, society and infrastuctures 5. The mathematical definition 6. Basic structural properties 7. Structural correlations of multiplex networks 8.

Communities 9. Centrality measures 10. Multilayer network models 11. Interdependent multilayer networks 12. Classical percolation, generalized percolation and cascades 13. Epidemic spreading 14. Diffusion 15. Synchronization, non-linear dynamics and control 16.

Opinion dynamics and game theory Appendix A. The Barabasi Albert model: the master equation Appendix B. Entropy and null models of single networks Appendix C. Growing multiplex networks: the master equation Appendix D. Percolation of interdependent networks Appendix E. Directed percolation of interdependent networks Appendix F. Immunization strategies on multiplex networks Appendix G. Spectrum of the Supra-Laplacian.