This work is intended to supplement and complement standard texts on continuum mechanics by drawing attention to physical assumptions implicit in continuum modelling. Particular attention is paid to linking continuum concepts, fields, and relations with underlying molecular behaviour via local averaging in both space and time. The aim is to clarify physical interpretations of concepts and fields and in so doing provide a sound basis for future studies. The contents should be of interest to engineers, mathematicians, and physicists who study macroscopic material behaviour.

The contents are the result of a long-standing study of formal and axiomatic presentations of continuum mechanics. Some of the issues were first addressed in courses delivered under the auspices of CISM (Udine, 1986, 1987), University of Cairo (1994, 1996), and AMAS (Warsaw, 2002; Bydgoszcz, 2003), and other topics treated in published papers. Here the opportunity has been taken to elaborate upon and extend earlier works and to present a unified, more readily accessible treatment of the subject matter.

Given the differing backgrounds of the intended readership, two extensive appendices have been included which develop relevant mathematical concepts and results. In particular, the use of direct (i.e., co-ordinate-free) notation is explained and related to that of Cartesian tensors.

No work exists in isolation: the author is above all indebted to his teachers Mort Gurtin and Walter Noll who introduced him to the mathematical precision and clarity of exposition to be found in modern continuum mechanics.