The first part of this book gives a detailed, self-contained and mathematically rigorous
exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions.
In particular, the conformal groups are determined and the appearance of the Virasoro algebra in
the context of the quantization of two-dimensional conformal symmetry is explained via the
classification of central
extensions of Lie algebras and groups. The second part surveys some more advanced topics of
conformal field theory, such as the representation theory of the Virasoro algebra, conformal
symmetry within string theory, an axiomatic approach to Euclidean conformally covariant
quantum field theory and a mathematical interpretation of the Verlinde formula in the
context of moduli spaces of holomorphic vector bundles on a Riemann surface.
The substantially revised and enlarged second edition makes in particular the second part
of the book more self-contained and tutorial, with many more examples given. Furthermore,
two new chapters on Wightman's axioms for quantum field theory and vertex algebras broaden
the survey of advanced topics. An outlook making the connection with most recent developments
has also been added.