I review the current status of the theory of Cosmic Inflation. My discussion covers the motivation and implementation of the idea, as well as an analysis of recent successes and open questions. There is a special discussion of the physics of ``cosmic coherence'' in the primordial perturbations. The issue of coherence is at the heart of much of the success inflation theory has achieved at the hands of the new microwave background data. While much of this review should be useful to anyone seeking to update their knowledge of inflation theory, I have also made a point of including basic material directed at students just starting research.

Lectures presented at the NATO Advanced Studies Institute ``Structure Formation in the Universe'', Cambridge 1999. To be published by Kluwer, R. Crittenden and N. Turok Eds. 28 Pages including 13 figures. 2nd verision includes a couple of additional references (Including the excellent new book by Liddle and Lyth) but is otherwise unchanged