infinitesimal 'spaces' is a serious issue in noncommutative (and commutative) geometry: they serve as a base of a Grothendieck-Berthelot crystalline theory and are of big importance for the D-module theory.

Can anybody point out the standard reference for this topic? I tried to look for it at nLab, but it seems it did not tell the reference in the language of algebraic geometry.

I am not very familiar with French,so the English manuscript is better, however, French one is fine.

Complexe Cotangent et Deformationsseems to be the standard reference, but Hartshorne also wrote a book relatively recently. – S. Carnahan♦ Jan 14 '10 at 19:11