p-mechanics as a physical theory: an introduction

This paper provides an introduction to p-mechanics, which is a consistent physical theory suitable for a simultaneous description of classical and quantum mechanics. p-mechanics naturally provides a common ground for several different approaches to quantization (geometric, Weyl, coherent states, Berezin, deformation, Moyal, etc) and has a potential for expansions into field and string theories. The backbone of p-mechanics is solely the representation theory of the Heisenberg group.