This volume can be considered as a supplementary volume to the three-volume "Handbook of Combinatorial Optimization" published by Kluwer. It can also be regarded as a stand-alone volume which presents chapters dealing with various aspects of the subject including optimization problems and algorithmic approaches for discrete problems. This handbook deals with several algorithmic approaches for discrete problems as well as with many combinatorial optimization problems. Each chapter in the handbook is expository in nature, but scholarly in treatment. The book is addressed not only to researchers in discrete optimization, but to all scientists in various disciplines who use combinatorial optimization methods to model and solve problems.