A complete, optional course on Graph Theory was first offered to Fourth Year Honours students of the Department of Mathematics, National University of Singapore in the academic year 1982/83. To those students taking this course, it was their first introduction to Graph Theory and so the standard of the course could not be set too high. However, since it was a fourth year Honours Course, the standard could not be too low. For this reason, I decided to use some existing textbooks for the basic results in the first term and to concentrate on only a few special topics in the second term in order to expose the students to some very recent results. This book eventually grew out from the lectures I gave to the students during the academic years 1982/83 and 1983/84.

More than seventy per cent of the materials in this book are taken directly from recent research papers. Each chapter (except chapter 1) gives an up-to-date account of a particular topic in Graph Theory which is very active in current research. In addition, detail of proofs of all the theorems are given and numerous exercises and open problems are included. Thus this book is not only suitable for use as a supplement to a course text at advanced undergraduate or postgraduate level, but will also, I hope, be of some help to researchers in Graph Theory. In fact, Mr. Chen Jing-Hui had written to inform me that by using my lecture notes in his fourth year Graph Theory course in Xiamen University, his students were able to do some research straightway.