This text provides a complete and thorough derivation of the mathematical theory of shell structures. Many books on shells only give the key equations or snippets of theory, skipping all of the mathematical steps required to solve for the key equations. This is understandable, because of the mathematical complexity of shell structures. Thus, the reader must just accept the design equations blindly, without achieving a complete understanding of shell theory. This book, therefore, fills this gap by providing a complete picture of shell theory. Class tested over three university post-graduate courses and one public course on shell structures, the book is mathematically intensive, but it written in an accessible style ideal for students of engineering mechanics in civil and mechanical engineers concentrations, as well as practicing structural engineers looking for a reference on shells.