Dilogarithms occur in physics in two different contexts, which so far do not
seem to be related: the evaluation of Feynman graphs and the arithmetic
properties of rational conformal field theories (CFTs). The lectures will
concentrate on the latter topic. We will discuss the structure of CFT
partition functions, in particular the characters of the corresponding W
algebras, the Galois group of rational CFTs and the relation between quantum
and conformal dimensions of the characters. We will explore the conjectured
relation between torsion elements of the Bloch group, the transformation of
characters under the modular group and level-rank duality. Finally we will
discuss massive deformations and the thermodynamic Bethe ansatz.
