**Description**

I intend this book to be/ firstly/ a introduction to calculus based on the hyperrealnumber system. In other words/ I will use infinitesimal and infinite numbers freely. Just as most beginning calculus books provide no logical justification for the real number system/ I will provide none for the hyperreals. The reader interested in questions of foundations should consult books such asAbraham Robinson's Non-standard Analysis or Robert Goldblatt's Lectures onthe Hyperreals. Secondly/ I have aimed the text primarily at readers who already have somefamiliarity with calculus. Although the book does not explicitly assume any prerequisites beyond basic algebra and trigonometry/ in practice the pace istoo fast for most of those without some acquaintance with the basic notions of calculus.

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