Introduction to Network Science: networks behind complex systems, characteristics of network science, societal and scientific impact of network science; Graph theoretic fundamentals: adjacency and adjacency representations, degree and degree sequence, paths and distance on a graph, center and diameter of a graph, Euler tours and Hamiltonian cycles, connectivity, graph drawing;Network properties: degree distribution, degree correlations, distance statistics, centrality, clustering coefficient, small-world effect, robustness; Network models and evolving networks: random networks, scale-free networks, Barabási–Albert (BA) model, Bose-Einstein condensation; Communities: clustering, modularity, overlapping communities, testing and characterizing communities; Network robustness: percolation theory, robustness of scale-free networks, attack tolerance, cascading failures, designing robust networks; Spreading phenomena: network epidemics, contact networks, immunization, epidemic prediction.