  The amount of data that is being gathered about cities is increasing in size
and specificity. However, despite this wealth of information, we still have
little understanding of what really drives the processes behind urbanisation.
In this thesis we apply some ideas from statistical physics to the study of
cities.
  We first present a stochastic, out-of-equilibrium model of city growth that
describes the structure of the mobility pattern of individuals. The model
explains the appearance of secondary subcenters as an effect of traffic
congestion, and predicts a sublinear increase of the number of centers with
population size. Within the framework of this model, we are further able to
give a prediction for the scaling exponent of the total distance commuted
daily, the total length of the road network, the total delay due to congestion,
the quantity of CO2 emitted, and the surface area with the population size of
cities. In the third part, we focus on the quantitative description of the
patterns of residential segregation. We propose a unifying theoretical
framework in which segregation can be empirically characterised. In the fourth
and last part, we succinctly present the most important---theoretical and
empirical---results of our studies on spatial networks.
  Throughout this thesis, we try to convey the idea that the complexity of
cities is -- almost paradoxically -- better comprehended through simple
approaches. Looking for structure in data, trying to isolate the most important
processes, building simple models and only keeping those which agree with data,
constitute a universal method that is also relevant to the study of urban
systems.
