1. Introduction; Part I. Random Network Models: 2. The Erdos-Renyi models; 3. Observations in real-world networks; 4. Models for complex networks; 5. Growing network models; Part II. Structure and Robustness of Complex Networks: 6. Distances in scale-free networks: the ultra small world; 7. Self-similarity in complex networks; 8. Distances in geographically embedded networks; 9. The network's structure - the generating function method; 10. Percolation on complex networks; 11. Structure of random directed networks - the bow tie; 12. Introducing weights: bandwidth allocation and multimedia broadcasting; Part III. Network Function: Dynamics and Applications: 13. Optimization of the network structure; 14. Epidemiological models; 15. Immunization; 16. Thermodynamic models on networks; 17. Spectral properties, transport, diffusion and dynamics; 18. Searching in networks; 19. Biological networks and network motifs; Part Appendix A. Probability theoretical methods; Appendix B. Asymptotics and orders of magnitude; Appendix C. Algorithms for network simulation and investigation; References; Index.