This book presents a modern continuum mechanics and mathematical framework to study shell physical behaviors and to formulate and evaluate finite element procedures. With a view towards the synergy that results from physical and mathematical understanding, the book focuses on the fundamentals of shell theories, their mathematical bases, and finite element discretizations. The complexity of the physical behaviors of shells is analyzed, and the difficulties in obtaining uniformly optimal finite element procedures are identified and studied. Some modern finite element methods are presented for linear and nonlinear analyses. In this second edition, the authors provide new developments in the field and, to make the book more complete, offer more explanations throughout the text, an enlarged section on general variational formulations, and new sections on 3D-shell models, dynamic analyses, and triangular elements.