This book introduces a trans-scale framework necessary for the physical understanding of breakdown behaviors and presents some new paradigm to clarify the mechanisms underlying the trans-scale processes. The book, which is based on the interaction of mechanics and statistical physics, will help to deepen the understanding of how microdamage induces disaster and benefit the forecasting of the occurrence of catastrophic rupture. It offers notes and problems in each part as interesting background and illustrative exercises. Readers of the book would be graduate students, researchers, engineers working on civil, mechanical and geo-engineering, etc. However, people with various background but interested in disaster reduction and forecasting, like applied physics, geophysics, seismology, etc., may also be interested in the book.