Introduction

The author aims to present a book on T-lines accessible for experts in all mentioned fields. The short survey below shows the mathematical and physical aspects of the theory of T-lines.

A n essential part of the complex analysis, particularly the classical theories of Nevanlinna and Ahlfors, deals with the number of zeros or, more generally, the number of a-points of the functions w(z), analytic or meromorphic, in given complex domains D or in the complex plane C. The a-points of w(z) are the solutions of the equation w(z) — a = 0 or, which is the same as the pre-images w~1(a) of the mapping given by w(z).