The second edition of these notes has been completely rewritten and
substantially expanded with the intention not only to improve the use of
the book as an int- ductory text to conformal ?eld theory, but also to
get in contact with some recent developments. In this way we take a
number of remarks and contributions by re- ers of the ?rst edition into
consideration who appreciated the rather detailed and self-contained
exposition in the rst part of the notes but asked for more details for
the second part. The enlarged edition also re?ects experiences made in
seminars on the subject. The interest in conformal ?eld theory has grown
during the last 10 years and several texts and monographs re?ecting
different aspects of the ?eld have been p- lished as, e. g., the
detailed physics-oriented introduction of Di Francesco, Mathieu, 1 and
Sen ´ echal ´ [DMS96*], the treatment of conformal eld theories as
vertex - gebras by Kac [Kac98*], the development of conformal ?eld
theory in the context of algebraic geometry as in Frenkel and Ben-Zvi
[BF01*] and more general by Beilinson and Drinfeld [BD04*]. There
is also the comprehensive collection of ar- clesbyDeligne, Freed,
Witten, andothersin[Del99*]aimingtogiveanintroduction to strings and
quantum ?eld theory for mathematicians where conformal ?eld theory is
one of the main parts of the text. The present expanded notes complement
these publications by giving an elementary and comparatively short
mathematics-oriented introduction focusing on some main principles.
