Special and general types group cohomology, nonabelian group cohomology, Lie group cohomology cohomology with constant coefficients / with a local system of coefficients Special notions Variants differential cohomology Extra structure Operations Theorems synthetic differential geometry Introductions geometry of physics: coordinate systems, smooth spaces, manifolds, smooth homotopy types, supergeometry Differentials Tangency The magic algebraic facts Theorems Axiomatics Models smooth algebra...