Where to start

1. A good introduction to infinitesimals is Keisler's calculus textbook Elementary Calculus: An Infinitesimal Approach available at https://people.math.wisc.edu/~hkeisler/calc.html

2. More advanced material, building on the calculus, can be found in my lecture notes available at https://u.cs.biu.ac.il/~katzmik/88-503.html based on Goldblatt's book (see below) and other sources.

3. A fine text in nonstandard analysis is Goldblatt, Robert. Lectures on the hyperreals. An introduction to nonstandard analysis. Graduate Texts in Mathematics, 188. Springer-Verlag, New York, 1998.

4. An introduction to axiomatic nonstandard analysis can be found at SPOT.