The field of mechanics which focuses on the study of the propagation of cracks in materials is referred as fracture mechanics. It comprises the analysis of flaws that is used to discover which structures are safe and which ones are liable to propagate as cracks and thereby, resulting in the failure of the flawed structure. Safe operation of a structure can be achieved through damage tolerance analysis. The two kinds of fracture mechanics are linear elastic fracture mechanics and elastic-plastic fracture mechanics. Linear elastic fracture mechanics covers the concepts of Griffith's criterion, Irwin's modification, stress intensity factor, strain energy release and crack tip plastic zone. Elastic-plastic fracture mechanics focuses upon the concepts of crack tip opening displacement (CTOD), R-curve, J-integral, cohesive zone model and transitions flaw size. This book will also provide interesting topics for research which interested readers can take up. It studies, analyses and upholds the pillars of fracture mechanics and its utmost significance in modern times. This book includes contributions of experts and scientists which will provide innovative insights into this field.