As the world embarks on new horizons in photonics and materials science, it is paramount that one's mathematical skills be honed. The primary objective of this book is to offer a review of vector calculus needed for the physical sciences and engineering. This review includes necessary excursions into tensor analysis intended as the reader's first exposure to tensors, making aspects of tensors understandable at the undergraduate level. A secondary objective of this book is to prepare the reader for more advanced studies in these areas.