Intended for graduate students and researchers in physics, chemistry, biology, and applied mathematics, this book provides an up-to-date introduction to current research in fluctuations in spatially extended systems. It offers a practical introduction to the theory of stochastic partial differential equations and gives an overview of the effects of external noise on dynamical systems with spatial degrees of freedom. The text begins with a general introduction to noise-induced phenomena in dynamical systems followed by an extensive discussion of analytical and numerical tools needed to get...