This comprehensive examination of the theory of valued and ordered fields describes their classical aspects, such as their arithmetic, topology, and Galois theory. It also includes material on the newly developed study of generalized Milnor K-rings. Efrat works through Abelian groups, then advances to valuations and orderings, including the tree of localities, topologies, complete fields, canonical variations and valuations of mixed characteristics, then describes Galois theory, including Hensel's Lemma and real closures, concluding with K-Rings, including fields, orderings, valuations, wild valued fields, decomposition and realization. Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)