Fracture mechanics is the science of predicting the load-carrying capabilities of cracked structures based on a mathematical description of the stress field surrounding the crack. The fundamental ideas stem from the work of Griffith, who demonstrated that the strain energy released upon crack extension is the driving force for fracture in a cracked material under load. This chapter provides a summary of Griffith’s work and the subsequent development of linear elastic and elastic-plastic fracture mechanics. It includes detailed illustrations and examples, familiarizing readers with the steps involved in determining strain energy release rates, stress intensity factors, J-integrals, R-curves, and crack tip opening displacement parameters. It also covers fracture toughness testing methods and the effect of measurement variables.