Graph algorithms are easy to visualize, and there already exists a variety of packages to animate the dynamics when solving problems from graph theory. However, it can be difficult to understand the ideas behind the algorithm from the dynamic display alone. CATBox consists of a software system for animating graph algorithms and a course book that we developed simultaneously. The software system presents both the algorithm and the graph, putting the user in control of the actual code that is executed. The course book, intended for readers at the advanced undergraduate or graduate level, features computer exercises and examples that replace the usual static pictures of algorithm dynamics. For this volume, we have chosen algorithms for classical problems from combinatorial optimization, such as minimum spanning trees, shortest paths, maximum flows, minimum cost flows, weighted and unweighted.