Today, Fracture Mechanics is a well known topic within the scientific community. Applications of Fracture Mechanics can be found in various fields ranging from solid mechanics and structures to materials sciences and computational mechanics. However, most of these results apply only to linear fracture mechanics of two-dimensional and homogeneous isotropic solids. Therefore there are still incompletely solved problems; such as non-linearity, frictional contact cracks, residual stresses in fracture mechanics, three-dimensional crack geometry, coupled cracked solid/fluid, etc. Recently, new topics related to crack detection based on different physical phenomena have appeared. This book is an attempt to present, in a unified manner, different topics of Continuum and Fracture Mechanics: energy methods, conservation laws, mathematical methods to solve two-dimensional and three-dimensional crack problems. Moreover, a series of new subjects is presented in a straightforward manner, accessible to under-graduate students. These new topics take into consideration the thermodynamics of continuous media, including thermal and dynamical aspects. In addition, the book introduces the notion of duality or symmetry in Solids Mechanics. The loss of symmetry is exploited to provide a unique and powerful tool, called the reciprocity gap functional introduced by the author's groups, to solve explicitly some important inverse problems arising in crack determination as well as in the earthquake inverse problem.With its emphasis, initially on physical or experimental back-grounds, and then on analysis and theoretical results, rather than on numerical computations, this monograph is intended to be used by students and researchers in solids mechanics, mechanical engineering and applied mathematics.