This course will start from an introduction to the field of complex networks. The introduction is somehow unusual in the way that it defines the concepts and then digs on then to illustrate their misusses and how to correct them. Concepts as "small-worldness", "scale-freeness", degree assortativity, and centrality, are among the ones studied. The course then continues with more advanced topics on network theory, such as the characterisation of degree heterogeneity, communicability and Euclidean geometry of networks as well as the extension of dynamics to consider "memory" and long-jumps that generate anomalous diffusive processes on networks. All the topics are richly illustrated with real-world examples.