Graph coloring is one of the oldest and best-known problems of graph theory. As people grew accustomed to applying the tools of graph theory to the solutions of real-world technological and organizational problems, new chromatic models emerged as a natural way of tackling many practical situations. Statistics show that graph coloring is one of the central issues in the collection of several hundred classical combinatorial problems. This book is devoted to problems in graph coloring, which can be viewed as one area of discrete optimization. Chapters are dedicated to various models and are largely independent of one another. In each chapter, the author highlights algorithmic aspects of the presented models, i.e., the construction of polynomial-time algorithms for graph coloring. This is an expanded and updated translation of the prizewinning book originally published in Polish, Optymalizacja dyskretna. Modele i metody kolorowania grafow. It is suitable for graduate students and researchers interested in graph theory.