  The constraining mathematical structure of the Coulomb branch of four
dimensional $\mathcal{N}=2$ supersymmetric theories is discussed. The
presentation follows a somewhat different route from other excellent reviews on
the subject and it is geared towards using this tool to classify four
dimensional $\mathcal{N}=2$ superconformal field theories. This is the writeup
of the lectures given at the Winter School "YRISW 2020" to appear in a special
issue of JPhysA.
