I Fundamentals -- 1. Definitions -- 2. Paths, Cycles and Trees -- 3. Hamilton Cycles and Euler Circuits -- 4. Planar Graphs -- 5. An Application of Euler Trails to Algebra -- Exercises -- Notes -- II Electrical Networks -- 1. Graphs and Electrical Networks -- 2. Squaring the Square -- 3. Vector Spaces and Matrices Associated with Graphs -- Exercises -- Notes -- III Flows, Connectivity and Matching -- 1. Flows in Directed Graphs -- 2. Connectivity and Menger's Theorem -- 3. Matching -- 4. Tutte's 1-Factor Theorem -- Exercises -- Notes -- IV Extremal Problems -- 1. Paths and Cycles -- 2. Complete Subgraphs -- 3. Hamilton Paths and Cycles -- 4. The Structure of Graphs -- Exercises -- Notes -- V Colouring -- 1. Vertex Colouring -- 2. Edge Colouring -- 3. Graphs on Surfaces -- Exercises -- Notes -- VI Ramsey Theory -- 1. The Fundamental Ramsey Theorems -- 2. Monochromatic Subgraphs -- 3. Ramsey Theorems in Algebra and Geometry -- 4. Subsequences -- Exercises -- Notes -- VII Random Graphs -- 1. Complete Subgraphs and Ramsey Numbers-The Use of the Expectation -- 2. Girth and Chromatic Number-Altering a Random Graph -- 3. Simple Properties of Almost All Graphs-The Basic Use of Probability -- 4. Almost Determined Variables-The Use of the Variance -- 5. Hamilton Cycles-The Use of Graph Theoretic Tools -- Exercises -- Notes -- VIII Graphs and Groups -- 1. Cayley and Schreier Diagrams -- 2. Applications of the Adjacency Matrix -- 3. Enumeration and Pólya's Theorem -- Exercises -- Notes -- Index of Symbols.