Higher-dimensional Contou-Carrere symbols

Higher-dimensional Contou-Carrere symbol is a deformation of the higher-dimensional tame symbol and the higher-dimensional residue which are important in the higher-dimensional class field theory of K. Kato, A. N. Parshin and others. I will give a review of results on higher-dimensional Contou-Carrere symbols, in particular, I will speak on its various definitions, including explicit formulas, and also about its universal property. The talk is based on joint papers with S. O. Gorchinskiy.