This chapter describes the use of Lie symmetries for algorithmically constructing invertible point mappings suitable to transform a given differential equation into an equivalent special form. In particular, some theorems are proved stating necessary and sufficient conditions for the transformation of (i) general systems of partial differential equations of arbitrary order to autonomous form; (ii) general first-order systems of partial differential equations to linear form; (iii) nonhomogeneous and/or nonautonomous quasilinear first-order systems of partial differential equations to homogeneous and autonomous form both in the case of \(2\times 2\) systems, and in the case of general systems involving an arbitrary number of independent and dependent variables; (iv) first-order nonlinear differential equations polynomial in the derivatives into autonomous first-order differential equations polynomially homogeneous in the derivatives. The proofs of the theorems are constructive, and the canonical variables associated to a set of Lie symmetries spanning a Lie algebra play the key role. Several examples coming from Physics are considered.