The book provides a general introduction to the theory of large
deviations and a wide overview of the metastable behaviour of
stochastic dynamics. With only minimal prerequisites, the book
covers all the main results and brings the reader to the most
recent developments. Particular emphasis is given to the
fundamental Freidlin-Wentzell results on small random perturbations
of dynamical systems. Metastability is first described on physical
grounds, following which more rigorous approaches to its
description are developed. Many relevant examples are considered
from the point of view of the so-called pathwise approach. The
first part of the book develops the relevant tools including the
theory of large deviations which are then used to provide a
physically relevant dynamical description of metastability. Written
to be accessible to graduate students, this book provides an
excellent route into contemporary research.
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