I was meaning to check out non-standard analysis too. Is this book any good?
The more I read this book the more I enjoy it. I'm not sure if it's me or the book but I'm making great progress through it. As an example I don't think I really understood the universal quantification of epsilon in the epsilon-delta definition of limits until I thought more seriously about the relationship between it and the infinitesimal definition of limits (and also without loss of generality arbitrarily restricting epsilon above). This is despite having gone threw the motions of many epsilon-delta proofs.