The aim of this course is to introduce Operator Algebras and provide examples and results by means of the constructions of C*-algebras associated to groupoids. For simplicity we will concentrate on aetial groupoids.
In the first part of the course, we will introduce the basic theory related to the abstract theory of C*-algebras.
In the second part, we intend to explain the basic theory of aetial groupoids and how we associate C*-algebras to them.
In the final part of the course we will study the relationship between C*-algebras of groupoids and C*-algebras of dynamical systems by constructing cross-products, thus providing examples that relate Operator Algebras to Dynamical Systems.

References:
Gerard J. Murphy, C*-Algebras and Operator Theory, Academic Press, 1990.
Dana Williams, – Crossed Product of C*-Algebras.
Alan L. T. Paterson, Groupoids, Inverse Semigroups, and their Operator. Algebras, Progress in mathematics, 1998.
Jean Renault, A groupoid approach to C*-algebras, Lecture Notes in Mathematics, vol. 793, Springer, Berlin, 1980.
Ruy Exel, Inverse semigroups and combinatorial C*-algebras, Bull. Braz. Math. Soc. (N.S.) 39 (2008), no. 2, 191-313.