an acyclic quiver. We first recall the notion of derived category, and we focus on examples in type $A_n$.

Section \[sect::2CYcat\] is devoted to the introduction of an abstract setting: that of $2$-Calabi–Yau triangulated categories with cluster-tilting objects. This setting contains that of cluster categories, and is the one used in these notes to study cluster characters.

Finally, cluster characters are introduced in Section \[sect::cluster-characters\], together with some of their properties leading to a categorification of cluster algebras.

The notes reflect a mini-course I gave at the CIMPA school in Mar del Plata, Argentina, in March 2016. Each section corresponds, more or less, to a one-hour lecture. I take this opportunity to thank the organizers of the CIMPA – ARTA V joint meeting during which this mini-course was given.

Quiver representations and submodule Grassmannians {#sect::representations}
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In this section, we define in an elementary way the notion of quiver representation, and introduce a projective variety, the *submodule Grassmannian*, whose points parametrize subrepresentations of a given representation.

Quiver representations
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Let $k$ be a field. We are interested in studying modules over $k$-algebras and their submodules. A convenient setting for this is that of quiver representations. There are many textbooks dealing 