Part I Theoretical Background of Fracture Mechanics Weight Function Methods.- Standardized Analytical Weight Function Method Based on Crack Opening Displacements.- Analysis and Discussions of Weight Function Methods Based on Multiple Reference Load Cases.- Accuracy Verifications of Various Weight Functions and Method Assessments.- Part II Weight Functions and Stress Intensity factors for Various Crack Geometries.- Center Crack(s) in Single Connected Domain.- Edge Crack(s) in Single Connected Domain.- Edge Crack(s) in Multiple Connected Domain.- Weight Function Method and Applications to Orthotropic Composite Material.- Weight Function Method and Fracture Analysis for Plates with Multiple Cracks.- Analytical Weight Functions and Mixed Mode Stress Intensity Factors for Mode II Cracks.- Weigh Functions for Three-dimensional Crack Problems.- Part III Various Engineering Applications of Weight Function Methods.- Weigh Function Analysis of Crack Problems with Thermal/Residual Stresses.- Computation of Crack Opening Displacements/Areas with Weigh Function Methods.- Analysis of Bridging, Cohesive Model and Crack Opening Stress with Weigh Function Methods.- Weigh Functions and Stress Intensity Factors for Complex Crack Geometry.- Application of Weigh Function Methods to Multiple Site Damage Analysis.- Determination of Un-cracked Stresses Using Inverse Weight Function Method.- Appendix.