This book is intended to present current knowledge in the field of mudflows. The type of material considered is mud at large, or, in rather more physical terms, a suspension containing a large fraction of colloidal particles, in general clay, which gives it a more or less onctuous aspect and in general controls the viscosity of the whole material. Typical examples of such materials are mud suspensions which flow in mountain streams after heavy rain, dirlling muds composed of waterbentonite mixtures with oil and grain, or red muds, the waster materials from the bauxite refining industry. the first part of the book has a fundamental character; it aims to provide all the basic elements (theoretical and practical) for appreciating the rheological properties (viscosity) of claywater or mud suspensions. From a more general point of view this part focuses in depth on the physics and rheology of suspensions. The second part concerns free surface flow problems for mud suspensions considered as yield stress fluids. In particualr, flow stability or impact, and, uniform, gradually varied, transient or unconfined mudflows are considered.