Whitham Deformations and Tau Functions in N = 2 Supersymmetric Gauge Theories

We review new aspects of integrable systems discovered recently in N=2 supersymmetric gauge theories and their topologically twisted versions. The main topics are (i) an explicit construction of Whitham deformations of the Seiberg-Witten curves for classical gauge groups, (ii) its application to contact terms in the u-plane integral of topologically twisted theories, and (iii) a connection between the tau functions and the blowup formula in topologically twisted theories.