The purpose of this textbook is to shed light upon the origins of fundamental  notions of Riemannian geometry, which makes up the framework of the  mathematical apparatus for the theory of general relativity. By introducing  arbitrary curvilinear coordinates in the conventional three-dimensional  Euclidean space, the appearance of contra- and covariant vectors is clarified, the  genesis of Christoffel's symbols and of covariant differentiation is brought to  light along with detailed explanation of their geometrical sense and meaning.  Among useful applications, the expressions for the differential operations of  vector analysis in curvilinear coordinates are derived, in particular, those in  orthogonal coordinates. Important examples include detailed derivations of  related expressions in spherical and cylindrical coordinates.  The textbook is intended for university students studying physics, as well as for  persons interested in the mathematical apparatus of general relativity; it also  may be helpful as a complete reference book with respect to the formulas of  vector differential operations in curvilinear coordinates.   —Montreal, 2016.—76 p.—$17.50.     ISBN: 978-0-9918732-1-0     Tensorial differential operations in curvilinear coordinates A textbook for university students studying Physics