The best book I have read on nonstandard analysis is "Lectures on the Hyperreals", by Goldblatt, which is excellent.
On the more practical end, Pétry's "Analyse Infinitésimale: une présentation non standard" is an extremely readable first-year-undergrad level textbook that shows you how simple first-year analysis is when approached this way (but it doesn't go much into what it actually is).
(Of course, per Thomas Forster IIRC, the purpose of a first-year course in real analysis is not actually to teach you about real analysis; so in my view this rather defeats the point. First-year real analysis is taught primarily to make sure you understand the difference between "for all x there exists y" and "there exists x such that for all y".)
On the more practical end, Pétry's "Analyse Infinitésimale: une présentation non standard" is an extremely readable first-year-undergrad level textbook that shows you how simple first-year analysis is when approached this way (but it doesn't go much into what it actually is).
(Of course, per Thomas Forster IIRC, the purpose of a first-year course in real analysis is not actually to teach you about real analysis; so in my view this rather defeats the point. First-year real analysis is taught primarily to make sure you understand the difference between "for all x there exists y" and "there exists x such that for all y".)