In study of NP-hard problems, many efforts have been made in design and analysis of approximation algorithms. Indeed, this is a hot research subject in computer science, not only in theory but also in systems because most of optimization problems raised in system research are NP-hard. This series of lectures is based on a newly published book (Ding-Zhu Du, Ker-I Ko, Xioadong Hu, Design and Analysis of Approximation Algorithms, Springer, 2011).