**Abstract: The notion of a Hilbert C*-module is a generalization of the notion of a Hilbert space. The first use of such objects was made by I. Kaplansky.
The research on Hilbert C*-modules began in the 70’s in the work of the induced representations of C*-algebras by M. A. Rieffel and the doctoral dissertation of W. L. Paschke.
It is also used to study Morita equivalence of C*-algebras, KK-theory of C*-algebras, operator K-theory, C*-algebra quantum group and theory of operator spaces.
In this lecture series, I would like to revisit the theory of Hilbert C*-module and discuss some of its recent exciting applications.
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**The following links are the video recordings and slides of this lecture series. **

**Lecture I**

**Lecture II**

**Lecture III**

**Lecture IV**

**Slides I**

**Slides II**