This paper is intended to serve as a model for for the first few chapters of future textbooks on continuum mechanics and continuum thermomechanics. It may be considered an update of the paper Lectures on the Foundations of Continuum Mechanics and Thermodynamics [N2] by one of us (W.N.), published in 1973, and an elaboration of topics treated in Part 3, entitled Updating the Non-Linear Field Theories of Mechanics, of the booklet [FC] by W.N..