Federer is perhaps best known for his treatise Geometric Measure Theory, published in 1969. Intended as both a text and a reference work, the book is unusually complete, general and authoritative: its nearly 600 pages cover a substantial amount of linear and multilinear algebra, give a profound treatment of measure theory, integration and differentiation, and then move on to rectifiability, theory of currents, and finally, variational applications. Nevertheless, the book's unique style exhibits a rare and artistic economy that still inspires admiration, respect—and exasperation. A more accessible introduction may be found in F. Morgan's book listed below.
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