This book presents elements of Geometric continuum Mechanics with application to rod theories. It presents a novel approach to this classical field. The scope of the book, as author states, is to introduce reader the differential geometric objects required for an intrinsic differential geometric description of a first gradient continuum, to combine this (geometric) approach with mechanical principles of a first gradient theory, to define beams as a constrained three dimensional bodies with constraints and to use the principle of virtual work to obtain the corresponding differential equations of motion. The author succeeds in the proposed goals. The special cases of Euler-Bernoulli Beam is treated as special case. In my opinion the book may be used in courses to the advanced undergraduate students that already have knowledge about the classical beam theories. Also it will be useful to the graduate students of Mechanics and the researchers in Mechanics.