Introduction, Conception and the Importance of Avalanche Research -- Granular Avalanches: Definition, Related Concepts and a Review of Classical Models -- A Continuum Mechanical Theory for Dense Avalanches Sliding Down Non-Trivial Topographies -- A Continuum Mechanical Theory for Granular Avalanches -- Rapid Flows of Dry Granular Masses in Arbitrarily Curved and Twisted Channels -- Exact and Semi-Exact Solutions of the Model Equations -- Exact Solutions for Flow Avalanches in Rotating Drums -- Shock Capturing Numerical Methods and Simulations of Free Surface Flows of Shallow Avalanches Sliding Over Curved and Twisted Channels -- Classical and High Resolution Shock-Capturing Numerical Methods in one Spatial Dimension -- Two-Dimensional Shock-Capturing Schemes for Avalanching Flow -- Avalanche Simulations over Curved and Twisted Channels -- Experimental Validation of the Theoretical Prediction with Different Measurement Techniques -- Experimental Findings and a Comparison with the Theory -- Particle Image Velocimetry for Free Surface Flow Avalanches -- Avalanche Experiments Using the PIV Measurement Technique -- Avalanche Protection and Defence Structures -- Protection Against Snow Avalanche Hazards -- Summary and Outlook. Avalanches, debris, mudflows and landslides are common and natural phenomena that occur worldwide, predominantly in mountainous regions. With an emphasis on snow avalanches, this book sets out to provide a survey and discussion about the motion of avalanche-like flows from initiation to run out. An important aspect of this book is the formulation and investigation of a simple but appropriate continuum mechanical model for the realistic prediction of geophysical flows of granular material. This will help the practitioners in the field to better understand the physical input and provide them with a tool for their work. Originating from many lectures the authors have given over the years, this instructive volume brings the reader to the forefront of research - an aim also supported by an extensive bibliogrpahy of almost 500 entries. Avalanche Dynamics should be accessible to, and is intended for, a broad readership of researchers, graduate students and practitioners with backgrounds in geophysics, geology, civil and mechanical engineering, applied mathematics and continuum physics.