Mechanics, Tensors & Virtual Works is designated to be used for a first one-semester course in Mechanics at the upper undergraduate level. It is intended for third year students in mathematics, physics and engineering. Most of the text comes from this level courses that the author taught at universities and engineering schools. In the particular case where such a course cannot be taught to engineers, a lot of introduced matters constitute the mathematical and mechanical bases of applied engineering mechanics.    The various chapters connect the notions of mechanics of first and second year with the ones which are developed in more specialized subjects as continuum mechanics at first, and fluid-dynamics, quantum mechanics, special relativity, general relativity, electromagnetism, stellar dynamics, celestial mechanics, meteorology, applied differential geometry, and so on.    This book is the ideal mathematical and mechanical preparation for the  above-mentioned specialized disciplines. This is a course of  Analytical Mechanics which synthesizes the notions of first level  mechanics and leads to the various mentioned disciplines by  introducing mathematical concepts as tensor and virtual work  methods. Analytical mechanics is not only viewed as a self-sufficient  mathematical discipline, but as a subject of mechanics preparing for  theories of physics and engineering too. One of the author's goals has  been to reduce the gap between first and second academic cycles. The  intensive use of the tensor calculus contributes to this  reduction. The main subjects of mechanics of the first academic cycle  are set in this context and let "handle" tensors. Many books relating  to the developments of tensor theory are either too abstract since  aimed at algebraists only, or too quickly applied to physicists and  engineers. The author has found a right compromise which allows to  bring closer these points of view; the book chapters are intended for  mathematicians, which will find an illustrated presentation of  mathematical concepts and solved problems in mechanics, and for  physics and engineering students too, since the mathematical  foundations are introduced in a practical way. It is the first time  that a mechanics course so much develops the tensor calculus by taking  into account the two previous sides! Besides the tensors, another  mathematical concept is systematically used and largely developed: The  virtual work. This notion is clearly introduced from the one of  virtual displacements and virtual velocities are also considered.    The introduction of mathematical "tools", namely tensors and virtual works, gives the mechanics treated subjects a great unity; these mathematical notions easily lead to geometrical ways in the frame of differential geometry, as well as to other methods in continuum mechanics for example. In Europe in particular, given its style, this book is aimed to contribute to teaching mechanics European programs, the scientific English language is simple and should be used as a common language for concerned students of all European countries. All definitions and propositions are written with the peculiar strictness proper to mathematicians, but they are always illustrated with numerous examples, remarks and exercises. The concise style of differential geometry books of the author is also found in this mechanics book. When writing this new book, the author had the following assertion fresh in his mind: Pedagogy contributes to Rigor.

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