Lectures on the theory of elliptic modular functions, Vol.1

First volume. Introduction. Developments concerning projective determinations of measure --
Part I. Foundations for the theory of the discontinuous groups of linear substitutions of one variable --
The discontinuity of groups with illustrations by simple examples --
The groups without infinitesimal substitutions and their normal discontinuity domans --
Further approaches to the geometrical theory of the properly discontinuous groups --
Part II. The geometrical theory of the polygon groups of zeta-substitutions --
Treatment of the rotation groups on the foundation of the normal discontinuity domains --
The canonical polygons and the moduli of the hyperbolic rotations groups --
Study of the circular-arc quadrangles without principal circle and remarks on other non-rotation groups --
Part III. Arithmetic methods of definition of properly discontinuous groups of zeta-substitutions --
The rotation subgroups inside the Picard groups and the associated binary quadratic forms --
The reproducing groups of ternary and quaternary quadratic forms --
A special kind of principal-circle and polyhedron groups with integral algebraic substitution coefficients --
Commentaries --
Commentary by Richard Borcherds on elliptic modular functions --
 Commentary by Jeremy Gray --
Commentary by William Harvey on automorphic functions --
Commentary by Barry Mazur --
Commentary by Series-Mumford-Wright --
Commentary by Domingo Toledo --
Commentaries by other mathematicians. Second volume. Part I. Narrower theory of the single-valued automorphic functions of one variable --
Concept, existence, and fundamental properties of the automorphic functions --
Form-theoretic discussions for the automorphic models of genus zero --
Theory of Poincaré series with special discussions for the models of genus zero --
The automorphic forms and their analytic representations for models of arbitrary genus --
Part II. Fundamental theorems concerning the existence of polymorphic functions on Riemann surfaces --
Proof of the principal-circle and the boundary-circle theorem --
Proof of the reentrant cut theorem --
An addition to the transformation theory of automorphic functions --
Commentaries by Richard Borcherds on elliptic modular functions --
Commentary by Jeremy Gray --
Commentary by William Harvey on automorphic functions --
Commentary by Barry Mazur --
Commentary by Series-Mumford-Wright --
Commentary by Domingo Toledo --
Commentaries by other mathematicians.