A class S theory is a 4d N=2 SUSY quantum field theory associated with a Riemann surface with/without punctures and a complex reductive group. It is not a conventional quantum field theory, given by lagrangian and a path integral. Nevertheless its existence predicts many mathematical assertions, e.g., S-duality of N=4 gauge theory, modularity of Vafa Witten partition function, AGT correspondence, and so on. After a brief explanation of a class S theory, I will talk a construction of its Higgs branch based on a ring object on the affine Grassmannian, which is my recent joint work with Braverman and Finkelberg.