Reaction-diffusion equations form a class of differential equations which in recent years have seen great steps forward both in the understanding of their analytical structure and in their application to a wide variety of scientific phenomena. This volume comprises a collection of articles on the theme of the theory and applications of reaction-diffusion equations. All the contributors are experts in their respective fields and together the articles will provide a coherent perspective to the current state of research in this area.Some of the articles survey particular applications such as in combustion theory, electrochemistry, and problems arising in the biological sciences such as cellular neurobiology and population dynamics. Other articles concentrate on the analytic behaviour of reatcion-diffusion equations such as blow-up, the formation of patterns, travelling wave solutions, and the Conley index.