differential modules over differential rings provides an introduction and reference for researchers in commutative and differential algebra and could be used as the basis for a graduate course or seminar. the book is best suited to an audience for whom the terminology of rings, modules, homomorphisms, and categories is already familiar. although the topic is rooted in differential algebra, and the book should be of interest to workers in that area, no particular prior knowledge of differential algebra is assumed. when it is necessary to use specialized results from differential algebra, especially picard--vessiot theory, the necessary definitions and theorems are supplied. features collects the basic definitions and results about differential modules in one convenient reference with uniform notation. accessible to readers who don't have extensive specialized knowledge of differential algebra or commutative ring theory. the first book of its kind dedicated exclusively to the topic in this generality. presents new formulations of previously published work as well as new results not previously published.