  The science of complex networks is a new interdisciplinary branch of science
which has arisen recently on the interface of physics, biology, social and
computer sciences, and others. Its main goal is to discover general laws
governing the creation and growth as well as processes taking place on
networks, like e.g. the Internet, transportation or neural networks. It turned
out that most real-world networks cannot be simply reduced to a compound of
some individual components. Fortunately, the statistical mechanics, being one
of pillars of modern physics, provides us with a very powerful set of tools and
methods for describing and understanding these systems. In this thesis, we
would like to present a consistent approach to complex networks based on
statistical mechanics, with the central role played by the concept of
statistical ensemble of networks. We show how to construct such a theory and
present some practical problems where it can be applied. Among them, we pay
attention to the problem of finite-size corrections and the dynamics of a
simple model of mass transport on networks.
