In the analytical study of fracture, many pieces of information can be learned. There is a brief history of the analytical study of fracture, including discussions about the pioneering theories from Griffith and Irwin. Also, there is a brief discussion about what makes these concepts analytical, rather than numerical. There is sections on both stress intensity and stress concentration, and how these concepts differ. Energy methods of fracture are discussed, such as strain energy release. There is a discussion about fatigue and how it relates to fracture. Finally, there is a statistical analysis of fracture and how it is beneficial to understanding fracture.