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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.

Large deviations. --- Stability. --- Dynamics --- Mechanics --- Motion --- Vibration --- Benjamin-Feir instability --- Equilibrium --- Deviations, Large --- Limit theorems (Probability theory) --- Statistics --- Mathematical statistics --- Large deviations --- Stability

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Large deviations --- Limit theorems (Probability theory) --- Phase transformations (Statistical physics) --- Tunneling (Physics) --- Penetration probability --- Quantum mechanical tunneling --- Tunnel effect --- Electric conductivity --- Solids --- Phase changes (Statistical physics) --- Phase transitions (Statistical physics) --- Phase rule and equilibrium --- Statistical physics --- Probabilities --- Deviations, Large --- Statistics --- Effet tunnel --- Transitions de phases --- Théorèmes des limites (théorie des probabilités) --- Grandes déviations --- Effet tunnel. --- Transitions de phases. --- Grandes déviations.