This paper offers a survey of several of the analytical methods recently applied in economics to the analysis of complex systems. Simply stated, the underlying idea is that macroeconomic variables should be considered as the result of a continuous process of interaction among heterogeneous agents. This view is clearly at odds with the standard approach, in which the microfoundation of macroeconomic models is obtained by recurring to an optimizing representative agent. Unfortunately, the mathematical machinery employed in dealing with social interactions might prove to be unfamiliar to a large portion of the profession. It follows that an effort in updating the traditional economists' toolbox is in order. This survey aims to accomplish this task by illustrating as simply as possible some basic notions of the mathematics of social interaction economics.