This is one book on infinitesimal calculus: https://www.amazon.com/Infinitesimal-Calculus-Dover-Books-Ma... .

However, and this is very amusing to me, it turns out that the process of automatic differentiation (see https://en.wikipedia.org/wiki/Automatic_differentiation, the section on dual numbers) works in exactly the same way. Just replace all of the primed symbols (u', v', etc.) with du, dv, etc. and dual numbers are isomorphic to infinitesimals (if I'm using that term correctly.)

Looks similar to this book, which I bought after a recommendation here: https://www.amazon.com/Infinitesimal-Calculus-Dover-Books-Ma...

While I haven't examined it closely, there's a well thought of, concise, no-fluff book on it: http://www.amazon.com/Infinitesimal-Calculus-Dover-Books-Mat...

One more book I found to be useful, at least for its introduction to the hyperreal number system: http://www.amazon.com/Infinitesimal-Calculus-Dover-Books-Mat... It's short and focused.