  In this paper we will first introduce the notion of affine structures on a
ringed space and then obtain several properties. Affine structures on a ringed
space, arising mainly from complex analytical spaces of algebraic schemes over
number fields, behave like differential structures on a smooth manifold.
  As one does for differential manifolds, we will use pseudogroups of affine
transformations to define affine atlases on a ringed space. An atlas on a space
is said to be an affine structure if it is maximal. An affine structure is
admissible if there is a sheaf on the underlying space such that they are
coincide on all affine charts, which are in deed affine open sets of a scheme.
In a rigour manner, a scheme is defined to be a ringed space with a specified
affine structure if the affine structures are in action in some special cases
such as analytical spaces of algebraic schemes. Particularly, by the whole of
affine structures on a space, we will obtain respectively necessary and
sufficient conditions that two spaces are homeomorphic and that two schemes are
isomorphic, which are the two main theorems of the paper. It follows that the
whole of affine structures on a space and a scheme, as local data, encode and
reflect the global properties of the space and the scheme, respectively.
