This book is a concise introduction to this basic toolbox, intended for studentsand professionals familiar with programming and basic mathematical language. Wehave used the book in undergraduate courses on algorithmics. In our graduate-levelcourses, we make most of the book a prerequisite, and concentrate on the starredsections and the more advanced material. We believe that, even for undergraduates,a concise yet clear and simple presentation makes material more accessible, as longas it includes examples, pictures, informal explanations, exercises, and some linkageto the real world.Most chapters have the same basic structure. We begin by discussing a problemas it occurs in a real-life situation. We illustrate the most important applications andthen introduce simple solutions as informally as possible and as formally as necessaryto really understand the issues at hand. When we move to more advanced andoptional issues, this approach gradually leads to a more mathematical treatment, includingtheorems and proofs. This way, the book should work for readers with a widerange of mathematical expertise. There are also advanced sections (marked with a *)where we recommend that readers should skip them on first reading. Exercises provideadditional examples, alternative approaches and opportunities to think about theproblems. It is highly recommended to take a look at the exercises even if there isno time to solve them during the first reading. In order to be able to concentrate onideas rather than programming details, we use pictures, words, and high-level pseudocodeto explain our algorithms. A section “implementation notes” links these abstractideas to clean, efficient implementations in real programming languages suchas C++ and Java. Each chapter ends with a section on further findings that providesa glimpse at the state of the art, generalizations, and advanced solutions.