Abstract: Transformational Methods are known to be one of the most efficient methods for finding exact solutions of Partial Differential Equations. In this talk we shall be concentrated on the differential transformations introduced by Darboux (DT). DT can be defined by so-called (m,n)-transformations which are Linear Partial Differential Operators without mixed derivatives. The (m,n)-transformations have interesting algebraic structure. The (m,n)-transformations can help us to solve the problem of the generality of the Darboux Wronskian formulas. Namely, Darboux stated and different authors proved for different cases that given some number of partial solutions, a DT can be defined via some Wronskians. Darboux believed that the reverse statement will be true "generally speaking". In this talk we show several results on our way to prove this reverse statement and to decide what is "the general case" in this context. The second part of the talk will be devoted to an invariant description of the DT. We start with an idea that in view of the said above it would be more efficient to defined DT in terms of invariants of the pair (L,z), where L is a Linear Partial Differential Operator, and z is an element of its kernel. We show that such invariants is in correspondence with solutions of certain PDE, and that instead of a chain of DT we can consider mappings of invariants.