This work stresses the unifying power of the geometrical framework in bringing together concepts from the different areas of physics. Common underpinnings of optics, elasticity, gravitation, relativistic fields, particle mechanics and others subjects are underlined. It attempts to extricate the notion of space currently in the physical literature from the metric connotation. It consists of a main text and a topical section. The main text introduces the mathematical ideas and serves as a guide to the topical section.