This brief monograph discusses various kinds of transformations, such as active and passive transformations, transformations in linear spaces and on abstract manifolds, Bäcklund transformations for partial differential equations (PDEs), and symmetry transformations of PDEs. An algebraic formalism for identifying symmetries of matrix-valued PDEs and studying their Lie-algebraic structure is described, based on abstract operators (characteristic derivatives) that admit a standard differential-operator representation in the case of scalar-valued PDEs.
