In this reprint of the 1967 original published by Gordon and Breach follow Artin's lecture notes originally prepared in 1950/51. Artin works through the theory of valuation, local class field theory, the elements of algebraic number theory and the theory of algebraic function fields of one variable. Assuming some knowledge of Galois theory and elementary understanding of point set topology, Artin covers general valuation theory in terms of valuations of a field, complete fields, e, f and n, ramification theory, and the different; in local class field theory he covers the first and second inequalities, the norm residue symbol, the existence theorem, and applications; in product formulae and function fields in one variable he covers preparation for the global theory, characterization of fields by the product formula, differentials in PF-fields, the Reimann-Roch theorem, constant field extensions, applications differentials in function fields and theorems on p-groups and Sylow groups. Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)