This is a comprehensive and state-of-the-art compendium of Newtonian-Eulerian (momentum/vectorial) mechanics, from an advanced and unified (i.e. continuum) viewpoint - "elementary" simply means no Lagrangean and no Hamiltonian theories / methods, otherwise the level is graduate and beyond; yet, the presentation is eminently readable and inclusive: the style is informal and the mathematics (this Achilles heel of modern mechanics books, especially of the applied/multi-body ones) has been kept to the simplest necessary for a work of this level and scope (see below) - all ahistorical and intuition-deadening jargon and formalisms have been intentionally avoided. As such, the book continues, renovates, and expands the grand tradition laid by such educational 20th century "elementary mechanics" classics as those written by (alphabetically): Butenin, Coe, Fox, Hamel, Lur'e, Magnus, Milne, Nielsen, Parkus, Pars, Synge, Szabo, Voigt et al.Specifically:The text is complemented by many remarks and completely solved nontrivial examples, along with many problems (all with their answers and many with hints).