The paper claims to give a systematic approach allowing one to obtain invertible variable transformations mapping nonlinear partial differential equations either into autonomous or linear form provided that some suitable conditions are satisfied. The procedure makes use of Lie group analysis so that some symmetries are required in order to obtain the required transformations, which are related to canonical variables. A linearization procedure is given in the last part of the paper valid for systems of partial differential equations that can be reduced to a single nonlinear equation linearly degenerate. The procedures are explained with some examples of physical interest