Ubiquitous in nature and everyday life, complex networks find application in a wide variety of technological, sociological and biological systems. This work describes topological properties of networks and processes occurring in them. How do networks behave? What are the main features of a network that govern their robustness or failure? Can the lessons of regular fractals be useful to the understanding of highly complex networks? How does dimensionality affect processes happening in them? After a thorough introduction giving explicit examples of a variety of real-world networks and their basic properties, this work describes several network models and their applications, including an extensive study of diffusion, the Einstein relation, and percolation in inhomogeneous complex networks.

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