Extremely interesting read! Definitely not for beginners. This is smooth infinitesimal analysis involving nilpotent non-invertible infinitesimals. These are non-zero infinitesimals whose "squares" are zero that are used in synthetic differential geometry. These are very unlike the infinitesimals used in Keisler's and Henle's books. Historically they are more like Nieuwentijdt's infinitesimals than Leibnitz infinitesimals. Highly recommended for those with some mathematical logic and set theory background,