Mechanism design is the subfield of game theory that deals with economic systems from the point of view of an optimizing designer. It involves optimization problems where the input to the problem is owned by self-interested parties (a.k.a. agents). The designer would like to come up with a protocol whereby the individual optimizations of the agents lead in equilibrium to optimization of the global objective. In this talk we will discuss some classical problems in mechanism design and the role of approximation in solving them. No knowledge of game theory is necessary.