Abstract: In the first part, we continue with the following topics: ---Clifford algebras, Clifford modules, spin structures, Dirac operators, Weitzenbock formula. ---Heat kernel and its asymptotic expansion, Gilkey's formula, McKean-Singer formula.

In the second part, Mitsuru Wilson (Western) will continue developing the theory of Hilbert C*-modules and discuss the KSGNS construction.