Tau functions are a central tool in the modern theory of integrable
systems. This volume provides a thorough introduction, starting
from the basics and extending to recent research results. It covers
a wide range of applications, including generating functions for
solutions of integrable hierarchies, correlation functions in the
spectral theory of random matrices and combinatorial generating
functions for enumerative geometrical and topological invariants. A
self-contained summary of more advanced topics needed to understand
the material is provided, as are solutions and hints for the
various exercises and problems that are included throughout the
text to enrich the subject matter and engage the reader. Building
on knowledge of standard topics in undergraduate mathematics and
basic concepts and methods of classical and quantum mechanics, this
monograph is ideal for graduate students and researchers who wish
to become acquainted with the full range of applications of the
theory of tau functions.
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