We refurbish our axiomatics of differential geometry introduced in
[Mathematics for Applications,, 1 (2012), 171-182]. Then the notion of
Euclideaness can naturally be formulated. The principal objective in this paper
is to present an adaptation of our theory of differential forms developed in
[International Journal of Pure and Applied Mathematics, 64 (2010), 85-102] to
our present axiomatic framework
