This text presents six mini-courses all devoted to interactions between representation theory
of algebras homological algebra and the new ever-expanding theory of cluster algebras. The
interplay between the topics discussed in this text will continue to grow and this collection
of courses stands as a partial testimony to this new development. The courses are useful for
any mathematician who would like to learn more about this rapidly developing field the primary
aim is to engage graduate students and young researchers. Prerequisites include knowledge of
some noncommutative algebra or homological algebra. Homological algebra has always been
considered as one of the main tools in the study of finite-dimensional algebras. The strong
relationship with cluster algebras is more recent and has quickly established itself as one of
the important highlights of today's mathematical landscape. This connection has been fruitful
to both areas-representation theory provides a categorification of cluster algebras while the
study of cluster algebras provides representation theory with new objects of study.The six
mini-courses comprising this text were delivered March 7-18 2016 at a CIMPA (Centre
International de Mathématiques Pures et Appliquées) research school held at the Universidad
Nacional de Mar del Plata Argentina. This research school was dedicated to the founder of the
Argentinian research group in representation theory M.I. Platzeck.The courses held
were:Advanced homological algebraIntroduction to the representation theory of
algebrasAuslander-Reiten theory for algebras of infinite representation typeCluster algebras
arising from surfacesCluster tilted algebrasCluster charactersIntroduction to K-theoryBrauer
graph algebras and applications to cluster algebras
