Soviet mathematician Georgi E. Shilov (1917-75) was a longtime Professor of Mathematics at Moscow State University and the author of several other successful Dover reprints.

This introduction to linear algebra and functional analysis offers a clear expository treatment, viewing algebra, geometry, and analysis as parts of an integrated whole rather than separate subjects. All abstract ideas receive a high degree of motivation, and numerous examples illustrate many different fields of mathematics. Abundant problems include hints or answers.