Lie groups of transformations for dealing with differential equations are specialized distinguishing independent and dependent variables. Then, it is needed to “prolong” the Lie group in order to determine the transformations of derivatives. The prolongation to the so-called jet spaceJet space (the space whose “coordinates” are the independent variables, the dependent variables, and the derivatives of the latter with respect to the former up to a finite order) is obtained by requiring that the contact conditions relating differentials of the dependent variables are preserved. Both the cases of ordinary and partial differential equations are analyzed. Then, the Lie infinitesimal criterion for computing the Lie symmetries admitted by a differential equation is formulated, and some examples with the explicit computations are given. It is also proved that the Lie symmetries of differential equations are the elements of a Lie algebra. Finally, contact transformations for scalar differential equations are properly introduced.