Béla Bollobás has taught at Cambridge University's Department of Pure Maths and Mathematical Statistics for over 25 years and has been a fellow of Trinity College for 30 years. Since 1996, he has held the unique Chair of Excellence in the Department of Mathematical Sciences at the University of Memphis. Bollobás has previously written over 250 research papers in extremal and probabilistic combinatorics, functional analysis, probability theory, isoperimetric inequalities and polynomials of graphs.

• 1. Probability theoretic preliminaries; 2. Models of random graphs; 3. The degree sequence; 4. Small subgraphs; 5. The evolution of random graphs - sparse components; 6. The evolution of random graphs-the giant component; 7. Connectivity and components; 8. Long paths and cycles; 9. The automorphism group; 10. The diameter; 11. Cliques, independent sets and colouring; 12. Ramsey theory; 13. Explicit constructions; 14. Sequences, matrices and permutations; 15. Sorting algorithms; 16. Random graphs of small order.

'… contains an enormous amount of material, assembled by one who has played a leading role in the development of the area.' Zentralblatt MATH