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A modern re-visitation of the consequences of the lack of an intrinsic notionof instantaneous 3-space in relativistic theories leads to a reformulation oftheir kinematical basis emphasizing the role of non-inertial frames centered onan arbitrary accelerated observer. In special relativity the exigence ofpredictability implies the adoption of the 3+1 point of view, which leads to awell posed initial value problem for field equations in a framework where thechange of the convention of synchronization of distant clocks is realized bymeans of a gauge transformation. This point of view is also at the heart of thecanonical approach to metric and tetrad gravity in globally hyperbolicasymptotically flat space-times, where the use of Shanmugadhasan canonicaltransformations allows the separation of the physical degrees of freedom of thegravitational field (the tidal effects) from the arbitrary gauge variables.Since a global vision of the equivalence principle implies that only globalnon-inertial frames can exist in general relativity, the gauge variables arenaturally interpreted as generalized relativistic inertial effects, which haveto be fixed to get a deterministic evolution in a given non-inertial frame. Asa consequence, in each Einstein's space-time in this class the wholechrono-geometrical structure, including also the clock synchronizationconvention, is dynamically determined and a new approach to the Hole Argumentleads to the conclusion that "gravitational field" and "space-time" are twofaces of the same entity. This view allows to get a classical scenario for theunification of the four interactions in a scheme suited to the description ofthe solar system or our galaxy with a deperametrization to special relativityand the subsequent possibility to take the non-relativistic limit.Comment: 33 pages, Lectures given at the 42nd Karpacz Winter School of  Theoretical Physics, "Current Mathematical Topics in Gravitation and  Cosmology", Ladek, Poland, 6-11 February 200

THE CHRONO-GEOMETRICAL STRUCTURE OF SPECIAL AND GENERAL RELATIVITY: A RE-VISITATION OF CANONICAL GEOMETRODYNAMICS