I learned the material first from Robinson's own book, simply titled Non-Standard Analysis, which I quite liked. A few years later, I read Goldblatt's Lectures on the Hyperreals (link to online PDF of full book), which I would heartily recommend. Having read that, I would very much recommend Non-Archimedean fields and asymptotic expansions by Robinson and Lightstone, which seems to be seriously under-appreciated [only a few model theorists seem to have recently dug it up]; not the best introduction to non-standard analysis, but to me the best introduction to its connections with the rest of analysis.

I learned the material first from Robinson's own book, simply titled Non-Standard Analysis, which I quite liked. A few years later, I read Goldblatt's Lectures on the Hyperreals (link to table of contents of the book), which I would heartily recommend. Having read that, I would very much recommend Non-Archimedean fields and asymptotic expansions by Robinson and Lightstone, which seems to be seriously under-appreciated [only a few model theorists seem to have recently dug it up]; not the best introduction to non-standard analysis, but to me the best introduction to its connections with the rest of analysis.