  These are expanded notes from three survey lectures given at the 14th
International Conference on Representations of Algebras (ICRA XIV) held in
Tokyo in August 2010. We first study identities between products of quantum
dilogarithm series associated with Dynkin quivers following Reineke. We then
examine similar identities for quivers with potential and link them to
Fomin-Zelevinsky's theory of cluster algebras. Here we mainly follow ideas due
to Bridgeland, Fock-Goncharov, Kontsevich-Soibelman and Nagao.
