Graphs -- Subgraphs -- Connected graphs -- Trees -- Separable and nonseparable graphs -- Tree-search algorithms -- Flows in networks -- Complexity of algorithms -- Connectivity -- Planar graphs -- The four-colour problem -- Stable sets and cliques -- The probabilistic method -- Vertex colourings -- Colourings of maps -- Matchings -- Edge colourings -- Hamilton cycles -- Coverings and packings in directed graphs -- Electrical networks -- Integer flows and coverings -- Unsolved problems.