The aim of the present monograph is to give a systematic exposition of
the theory of algebraic surfaces emphasizing the interrelations between
the various aspects of the theory: algebro-geometric, topological and
transcendental. To achieve this aim, and still remain inside the limits
of the allotted space, it was necessary to confine the exposition to
topics which are absolutely fundamental. The present work therefore
makes no claim to completeness, but it does, however, cover most of the
central points of the theory. A presentation of the theory of surfaces,
to be effective at all, must above all give the typical methods of proof
used in the theory and their underlying ideas. It is especially true of
algebraic geometry that in this domain the methods employed are at least
as important as the results. The author has therefore avoided, as much
as possible, purely formal accounts of results. The proofs given are of
necessity condensed, for reasons of space, but no attempt has been made
to condense them beyond the point of intelligibility. In many instances,
due to exigencies of simplicity and rigor, the proofs given in the text
differ, to a greater or less extent, from the proofs given in the
original papers.