In this paper, we give general definitions of non-commutative jets in the local and global situation using square zero extensions and derivations. We study the functors Exan(subscript k) (A, I), where A is any k-algebra, and I is any left and right A-module and use this to construct affine non-commutative jets. We also study the Kodaira-Spencer class KS (L) and relate it to the Atiyah class.