Aimed at senior undergraduates and graduate students in science and biomedical engineering, this text explores the architecture of a cell's envelope and internal scaffolding, and the properties of its soft components. The book first discusses the properties of individual flexible polymers, networks and membranes, and then considers simple composite assemblages such as bacteria and synthetic cells. The analysis is performed within a consistent theoretical framework, although readers can navigate from the introductory material to results and biological applications without working through the intervening mathematics. This, together with a glossary of terms and appendices providing quick introductions to chemical nomenclature, cell structure, statistical mechanics and elasticity theory, make the text suitable for readers from a variety of subject backgrounds. Further applications and extensions are handled through problem sets at the end of each chapter and supplementary material available on the Internet.