This book presents derivations of the basic equations of mechanics in invariant form and specialisations of the governing equations of thermoelastic, magnetothermoelastic, vibration and buckling analysis to both thin and thick shells and spheres made of functionally graded materials. The results presented herein may be treated as a benchmark for checking the validity and accuracy of other numerical solutions. Despite a number of existing texts on the theory and analysis of plates and/or shells, up until this point there has not been a single book that is devoted entirely to the analysis of inhomogeneous isotropic and functionally graded shells and spheres.