Providing a comprehensive set of problem studies that builds on the authors' expertise and class-tested material, this useful manual offers a guided exploration of methods and techniques to assess problem complexity in the study and design of algorithms. The first part of the text presents background material on the study of algorithms and algorithm design, addressing such basic paradigms as divide-and-conquer, dynamic programming, and greedy algorithms. It also covers NP-completeness and beyond NP-completeness, including approximation results. The second part of the text is devoted to case studies that exploit tools and techniques for assessing problem complexity.