This one sounds like what you want:

Arkeryd, Cutland and Henson: Nonstandard Analysis, Theory and Applications.

I took a course as undergraduate which followed (parts of) this book - I first accompanied it with the more friendly written Goldblatt to get some feeling for the subject, then switched to this one, when I also started finding Goldblatt too "verbose". It found it very well readable.

Cutland has produced other enjoyable writings and there also is Loeb, Wolff: Nonstandard analysis for the working mathematician, which I haven't read but which follows a very similar agenda at a very similar pace, according to the table of contents.

Enjoy!