  This is an introduction to some aspects of Fomin-Zelevinsky's cluster
algebras and their links with the representation theory of quivers and with
Calabi-Yau triangulated categories. It is based on lectures given by the author
at summer schools held in 2006 (Bavaria) and 2008 (Jerusalem). In addition to
by now classical material, we present the outline of a proof of the periodicity
conjecture for pairs of Dynkin diagrams (details will appear elsewhere) and
recent results on the interpretation of mutations as derived equivalences.
