We outline the basic methods of algorithm design and analysis that have found application in the manipulation of discrete objects such as lists, arrays, sets, graphs, and geometric objects such as points, lines, and polygons. We begin by discussing recurrence relations and their use in the analysis of algorithms. Then we discuss some speciﬁc examples in algorithm analysis, sorting and priority queues. In Sections 1.3 through 1.6, we explore three important techniques of algorithm design-divide-and-conquer, dynamic programming, and greedy heuristics. Finally, we examine establishing lower bounds on the cost of any algorithm for a problem.