Description: Networks surround us, from social networks to protein-protein interaction networks within the cells of our bodies. The theory of random graphs provides a necessary framework for understanding their structure and development. This text provides an accessible introduction to this rapidly expanding subject. It covers all the basic features of random graphs - component structure, matchings and Hamilton cycles, connectivity and chromatic number - before discussing models of real-world networks, including intersection graphs, preferential attachment graphs and small-world models. Based on the authors own teaching experience, it can be used as a textbook for a one-semester course on random graphs and networks at advanced undergraduate or graduate level. The text includes numerous exercises, with a particular focus on developing students skills in asymptotic analysis.