Graphs drawn on two-dimensional surfaces have always attracted
researchers by their beauty and by the variety of difficult
questions to which they give rise. The theory of such embedded
graphs, which long seemed rather isolated, has witnessed the
appearance of entirely unexpected new applications in recent
decades, ranging from Galois theory to quantum gravity models, and
has become a kind of a focus of a vast field of research. The book
provides an accessible introduction to this new domain, including
such topics as coverings of Riemann surfaces, the Galois group
action on embedded graphs (Grothendieck's theory of "dessins
d'enfants"), the matrix integral method, moduli spaces of curves,
the topology of meromorphic functions, and combinatorial aspects of
Vassiliev's knot invariants and, in an appendix by Don Zagier, the
use of finite group representation theory. The presentation is
concrete throughout, with numerous figures, examples (including
computer calculations) and exercises, and should appeal to both
graduate students and researchers.
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