  We define a class of quadratic differential algebras which are generated as
differential graded algebras by the elements of an Euclidean space. Such a
differential algebra is a differential calculus over the quadratic algebra of
its elements of differential degree zero. This generalizes for arbitrary
quadratic algebras the differential graded algebra of exterior polynomial
differential forms for the algebra of polynomial functions on $\mathbb R^n$. We
investigate the structure of these differential algebras and their connection
with the Koszul complexes of quadratic algebras.
