This book describes a family of state-of-the-art numerical and semi-analytical techniques for determining stress intensity factors for cracks; the quantities which determine and control the fatigue life of engineering components. Fatigue problems are dominated by behaviour of the crack when it is short, and in the neighbourhood of the source of nucleation, as this is where the majority of the life is used up. A kwledge of crack-tip stress intensity factors in this regime is paramount. The techniques described in this book are very efficient methods of determining stress intensity factors with great precision and computational efficiency. This will allow for accurate estimates of component life and inspection intervals.