This book proposes a new general setting for theories of bodies with microstructure when they are described within the scheme of the con­ tinuum: besides the usual fields of classical thermomechanics (dis­ placement, stress, temperature, etc.) some new fields enter the picture (order parameters, microstress, etc.). The book can be used in a semester course for students who have already followed lectures on the classical theory of continua and is intended as an introduction to special topics: materials with voids, liquid crystals, meromorphic con­ tinua. In fact, the content is essentially that of a series of lectures given in 1986 at the Scuola Estiva di Fisica Matematica in Ravello (Italy). I would like to thank the Scientific Committee of the Gruppo di Fisica Matematica of the Italian National Council of Research (CNR) for the invitation to teach in the School. I also thank the Committee for Mathematics of CNR and the National Science Foundation: they have supported my research over many years and given me the opportunity to study the topics presented in this book, in particular through a USA-Italy program initiated by Professor Clifford A. Truesdell. My interest in the field dates back to a period of collaboration with Paolo Podio-Guidugli and some of the basic ideas came up during our discussions.

Introduction.- I General Properties.- The Model for the Microstructure.- The Notion of Observer.- Continua with Microstructure.- Invariance Properties.- Conservation of Mass: Kinetic Energy.- Inertia.- Dynamic Equations of Balance.- Balance of Moment of Momentum.- Boundary Conditions: Change of Variables.- The Conservative Case in Statics.- Perfect Fluids with Microstructure.- Rules of Invariance and the Balance of Moment of Momentum: Variational Principles in Dynamics.- Internal Constraints: Continua with Latent Microstructure.- II Special Theories.- Continua with One-Dimensional Microstructure: Continua with Voids.- Liquids with Bubbles.- Dilatant Granular Materials.- The Perfect Korteweg Fluid.- Continua with Vectorial Microstructure.- Uniaxial Liquid Crystals.- Continua with Affine Microstructure.- Micromorphic Elastic Continua: Bodies with Continuous Distribution of Dislocations.- The Continua of Cosserat.- Biaxial Nematic Liquid Crystals.- III Thermodynamics.- Balance Equations.- Interpretation of the Equations of Balance.- Thermodynamics of Continua with Latent Microstructure.- Comparison with the Traditional Class of Hyperelastic Bodies.- IV Mathematical Problems Posed by the Theory.- The Influence of the Topological Properties of the Manifold M.- Further Remarks on the Topological Theory of Defects.- Existence of Singular Solutions in Statics.- Phase Transitions.- Droplets of Perfect Liquids with Microstructure.