In many systems in Nature constituents form a highly interconnected network, offering a level of complexity that makes them practically untreatable with traditional methods. Examples include the metabolic network in a cell, social networks, business networks, the world wide web or the Internet. The inability of contemporary science to describe these systems currently limits advances in many disciplines, ranging from molecular biology to computer science. The objective of the present proposal is to capitalize on the increasing availability of topological information on real networks to uncover the basic mechanisms that determine the network topology. Our exploration is driven by the conviction that the emergence and the evolution of complex networks are governed by generic mechanisms that are common to many systems. To achieve our goal we propose a research program composed of three steps. First we plan to identify quantities that uniquely characterize the network topology, aiming to develop a set of measures, that eventually will allow us to construct a network with unique topological properties. Second, we plan to investigate the concept of universality: what are the mechanisms that determine the scaling exponents and the topology of the network. Third, we plan to study to which degree can a network be reconstructed from partial topological information.