Modal Logic is a branch of logic with applications in many related disciplines such as computer science, philosophy, linguistics and artificial intelligence. Over the last twenty years, in all of these neighbouring fields, multi-dimensional modal systems have been developed. This book treats multi-dimensional modal logics in a uniform way, linking their mathematical theory to the research tradition in algebraic logic. It defines and discusses a number of systems in detail, focusing on such aspects as expressiveness, definability, axiomatics, decidability and interpolation.