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.