The period since the publication of the first edition of this book has seen the theory of random graphs go from strength to strength. Indeed, its appearance happened to coincide with a watershed in the subject; the emergence in the subsequent few years of singnificant new ideas and tools, perhaps most noteably concentration methods, has had a major impact. It could be argued that the subject is now qualitatively different, insofar as results which would previously have been inaccessible are now