Klassenkörpertheorie. Ausbreitung einer Vorlesung vom Sommersemester 1932 und eines Teiles der Fortsetzung vom Wintersemester 1932/33 an der Universität Marburg.

Marburg: Helmut Hasse, 1932. FIRST PRINTING. Typed on rectos only; mimeographed. Numerous diagrams throughout. Contemporary blue calf over boards, author and title in gilt on spine. First printing of an elaboration of lectures given by Hasse (1898–1979) on class field theory. The lectures were first presented at the summer semester 1932 and a part of the continuation from the winter semester 1932/1933 at the University of Marburg.

In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field. For abelian extensions, the theory was developed between roughly 1850 and 1930 by Kronecker, Weber, Hilbert, Takagi, Artin, Hasse, and others. Hasse gave the first proof of local class field theory, proved the Hasse (local-global) principle for all quadratic forms over number fields, and contributed to the classification of central simple algebras over number field.

OCLC locates 4 copies of this mimeograph in America (Yale, Chicago, Brown, Ohio State).