The book offers a new general setting for theories of bodies with microstructure (or ordered media as they are also called) when they are described within the scheme of the Continuum: then besides the usual fields of classical thermomechanics (displacement, 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 followed already lectures on the classical theory of continua as an introduction to special topics: materials with voids, liquid crystals, meromorphic continua (all topics that are briefly mentioned here as examples). Research students studying continuum theories of new materials will find the book of help, as it may offer the appropriate framework for new developments and a link between apparently disparate themes such as the topological theory of defects, phase transitions and boojums.