Differential algebra provides an algebraic viewpoint on nonlinear differential systems. The motivating questions for this talk are: How do we define the general solution of a nonlinear equations What are the conditions for a differential system to have a solution How do we measure the "degrees of freedom" for the solution set of a differential system Theory and algorithms for those are extensions of commutative algebra (prime ideal decomposition, Hilbert polynomials) and Groebner bases techniques. The library diffalg in Maple supports this introduction to constructive differential algebra. It has been developed by F. Boulier (1996) and the speaker afterwards. A recent extension of differential algebra to non-commutative derivations, and its implementation in diffalg, allow to treat systems bearing on differential invariants.