Deformed Spacetime : Geometrizing Interactions in Four and Five Dimensions This volume provides a detailed discussion of the mathematical aspects and physical applications of a new geometrical structure of space time based on a generalization ( deformation ) of the usual Minkowski space as supposed to be endowed with a metric whose coefficients depend on the energy. This new five dimensional scheme (Deformed Relativity in Five Dimensions DR5) represents a true generalization of the usual Kaluza Klein (KK) formalism. This volume provides a detailed discussion of the mathematical aspects and the physical applications of a new geometrical structure of space time based on a generalization (&quot;deformation&quot;) of the usual Minkowski space as supposed to be endowed with a metric whose coefficients depend on the energy. Such a formalism (Deformed Special Relativity DSR) allows one to account for breakdown of local Lorentz invariance in the usual special relativistic meaning (however Lorentz invariance is recovered in a generalized sense) to provide an effective geometrical description of the four funda