This new third edition has again been thoroughly revised, even though the changes are not as extensive as in the second edition. Of course, the general aims of the book have remained the same.

"In particular, I have added some additional material, namely two new sections concerning graphical codes (which provides a less obvious area of application and, as I hope, might also interest the reader in the important field of coding theory) and about two dozen further exercises (as usual, with solutions). I have also discussed and referenced recent developments, especially for the travelling salesman problem, where truly impressive new world records have been achieved.
Moreover, the presentation of the material has been improved in quite a few places, most notably in the chapters on shortest paths and colorings. In addition to this, many smaller changes and corrections have been made, and the proof of several theorems have been rewritten to make them more transparent, or more precise. Again, I thank my students and assistants for their attention and interest as well as the input they provided. Moreover, I am indebted to several readers who alerted me to some (fortunately, more or less minor) problems; and I am, of course, also grateful for the encouraging comments I have received." Dieter Jungnickel