Polynomial automorphisms, quantization, and Jacobian conjecture related problems. I. Introduction

The purpose of this review is the collection and systematization of results concerning the quantization approach to the some classical aspects of non-commutative algebras, especially to the Jacobian conjecture. We start with quantization proof of Bergman centralizing theorem, then discourse authomorphisms of INd-schemes authomorphisms, then go to aproximation issues. Last chapter dedicated to relations between $PI$-theory Burnside type theorems and Jacobian Conjecture (Jagzev approach). This issue contains the first part of the work; continuation will be published in future issues.