This is a comprehensive and state-of-the-art compendium of classical or Newtonian (non relativistic and non quantum) mechanics from an advanced and unified viewpoint, namely, from the continuum, or field, form of the fundamental principles of linear and angular momentum of Euler, Cauchy, Hamel et al. The title adjective "elementary" simply means no Lagrangean and no Hamiltonian theories and methods. Yet, in spite of its high level, this extensive work of more than 1450 dense pages of text, and more than 350 pages of galleries is eminently readable and inclusive. The overall style is informal, all ahistorical and intuition-deadening jargon and formalisms ("epsilonics") have been intentionally avoided. The mathematics, typically an Achilles heel of modern mechanics books, especially those in applied or multi-body mechanics, has been kept to the simplest necessary for a work of this level and scope. As such, the book continues, renovates, and expands the grand tradition laid by such educational 20th century "elementary mechanics" classics as those written by Butenin, Coe, Fox, Hamel, Loitsianskii, Lur'e, Magnus, Milne, Nielsen, Parkus, Pars, Stäckel, Synge, Szabó, Voigt, among others.Specifically: The book opens with a unique part on the history of theoretical and applied mechanics from classical antiquity (Greece) to late 20th century, including many hundreds of portraits and photos of famous researchers in mechanics (some appearing in public for the first time), and select pages from their most famous works.;Then, to make this volume as self-contained as possible and establish better rapport with its readers, thus saving them precious time and energy, an extensive, handbook-like exposition of the necessary mathematics is supplied; i.e., algebra + calculus of Cartesian vectors and tensors, and linear algebra / matrices in both indicial and direct notations.;Afterwards, mechanics proper is treated (in order of increasing complexity): first, particle and general mechanics; then, the rigid body; and last, general continua with an introduction to elastic solids. All basic concepts and principles are presented in general form, exact equations as well as their approximations. The emphasis is on ideas and results of permanent interest.;The text is complemented, clarified, and enriched by many remarks, completely solved nontrivial examples, and problems, all of the latter with their answers and many with hints. It will be of interest to senior undergraduate and graduate students and teachers in and out of the academia, in the areas of engineering (aero&astro, civil, mechanical, controls), theoretical and applied mechanics, physics, applied mathematics, science history and others, for class reference and self study. Nothing equivalent or comparable to it has ever appeared, in any language, in the mechanics literature.