As the field of difference equations expands, the discovery of general new methods of study & analysis can aid considerably in the evolution of the subject. This book presents a new systematic approach to reduction of order by changing variables. The author builds a step-by-step framework by defining the context for a formalization based on semiconjugacy & then presenting results for large classes of difference equations to which the new methods apply. The text shows that the characteristic polynomial & both the complimentary & particular solutions can be calculated directly from additively separable form