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 unctuous aspect and in general controls the viscosity of the whole material. Examples of such materials are mud suspensions which flow in mountain streams after heavy rain, drilling muds composed of waterbentonite mixtures with oil and grain, or red muds, the waste materials from the bauxite refining industry. The first part of the book aims to provide all basic elements for appreciating the rheological properties of claywater or mud suspensions. The second part concerns free surface flow problems for mud suspensions considered as yield stress fluids. Flow stability, similarity or impact, and, uniform, gradually varied, transient or unconfined mudflows are considered.