Discrete optimization problems everywhere, from the traditional problem of planning operations research, such as scheduling, facility location, and network design, to computer science problems in the database, to issue advertisements in viral marketing. This book shows how to design the algorithm approach: efficient algorithms that find provably near-optimal solution. The book is organized around the central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear programming and semidefinite, and randomization. Designed as a textbook for undergraduate-level algorithms, this book will also serve as a reference for researchers who are interested in the solution heuristic discrete optimization problems.