Contents 1. Introduction on Very High Cycle Fatigue. 2. Plasticity and Initiation in Gigacycle Fatigue. 3. Heating Dissipation in the Gigacycle Regime. About the Authors Claude Bathias is Emeritus Professor at the University of Paris 10-La Defense in France. He started his career as a research engineer in the aerospace and military industry where he remained for 20 years before becoming director of the CNRS laboratory ERA 914 at the University of Compiègne in France. He has launched two international conferences about fatigue: International Conference on the Fatigue of Composite Materials (ICFC) and Very High Cycle Fatigue (VHCF).