Mechanics of continua has atracted a gat interest in our time, which is proved by numerous publications on the matter, on whitch autors like A more than C. Eurigen, C. Trueesdell, L. I. Sedov, Green –Zenna treat the theory in general and develop particular topics. The complexity of this fiels of study creates a great difficulty of formulation. The present work develops a consistent intrinsic notation, on which the relations of variables describing space and time are of clear characterization allowing to produc a general formulation of the theory of continuum Mechanics. This study is done a general manner, admitting finite deformations beig the results obtained simplified by approximations. In the first chapter we study the geometry of deformation, whitch receiveis a geometrical interpratation, and we obtain the invariants wich be needed for developing the constittutive relations. We study kinematics of the motion, relate deformations and velocities and finish with the compatibility equations. Chapter two studies physical principles followed by a continum inmotion, allowing us to obtain a system of equations that is enough to problems formulation. In chapter three we develop a general model of elastic media and particularize the results as far as to reach the classical elasticity, where as, in chapter four, general equations are applied to describe the motion of ideak and viscous fluids. We finish our work with two applications, one in the field of Elasticity and the other in Fluid Mechanics.