This comprehensive compendium provides a rigorous framework to tackle the daunting challenges of designing correct and efficient algorithms. It gives a uniform approach to the design, analysis, optimization, and verification of algorithms. The volume also provides essential tools to understand algorithms and their associated data structures. This useful reference text describes a way of thinking that eases the task of proving algorithm correctness. Working through a proof of correctness reveals an algorithm's subtleties in a way that a typical description does not. Algorithm analysis is presented using careful definitions that make the analyses mathematically rigorous. Algorithms are presented in a pseudo language defined with enough rigor to facilitate both performance analyses and correctness proofs. The essence of an algorithm is not tied to a particular programming language; hence, we have chosen a computational model and corresponding notation that we feel are appropriate for communicating algorithms to humans.