The field of algorithms is now a well-established part of computer science and mathematics, with its theoretical elegance and practical importance. On the one hand, computer practitioners can directly use good algorithms in complex programming projects. On the other hand, efficient algorithms often pose a challenging mathematical problem because their analysis uses deep mathematical results from different fields. Thus the modern study of algorithms is based on an interplay between their computational and mathematical aspects. The goal of this book is to lay down foundations for this fascinating area. In keeping with this goal, we have attempted to present some of the most fundamental methods for algorithm construction. In particular, the book introduces a number of paradigms and techniques useful for designing and analyzing data structures and algorithms.