Fundamentals of elasticity and fracture mechanics -- Yue's solution of a 3D multilayered elastic medium -- Yue's solution-based boundary element method -- Application of the Yue's solution-based BEM to crack problems -- Analysis of penny-shaped cracks in functionally graded materials -- Analysis of elliptical cracks in functionally graded materials -- Yue's solution-based dual boundary element method -- Analysis of rectangular cracks in the FGMs -- Boundary element analysis of fracture mechanics in transversely isotropic bi-materials.