From a preface: ..College algebra has a basic unity. It should consist of, study of the number systems of elementary mathematics, olynomials and allied functions, algebraic identities, equaions, and systems of equations. The unity of the present ext is achieved by fitting the standard topics of college algebra into this pattern...

About the author Adrian Albert, one of the foremost algebraists of the world and President of the American Mathematical Society from 1965 to 1967. Albert was a first generation American and a second generation American mathematician following that of E. H. Moore, Oswald Veblen, L. E. Dickson and G. D. Birkhoff. He earned a B.S. degree in 1926, an M.S. degree in 1927, and a Ph.D. in 1928. His advisor for his master's and his doctoral dissertations was Leonard Eugene Dickson. After his doctorate. Albert spent a year at Princeton University as a National Research Council Fellow. He was attracted to Princeton by that great master of associative algebra theory, J. H. M. Wedderburn, who was then a professor at the university. Albert returned to Princeton in 1933, this time as one of the first group of temporary members of the Institute for Advanced Study. Except for two years (1929-1931) as an Instructor at Columbia University and a number of visiting professorships (at Rio de Janeiro, Buenos Aires, University of Southern California, Yale, and the University of California at Los Angeles) all of Albert's academic career was spent at the University of Chicago. In 1960 he was named Eliakim Hastings Moore Distinguished Service Professor, and he served as Chairman of the Department of Mathematics for three years until he became Dean of the Division of Physical Sciences in 1962. He held this position until 1971 when he reached the mandatory retirement age of sixty-five for the deanship. Albert pushed forward the theory of multiplication algebras of Riemann matrices until he achieved a complete solution of the central problem. For this achievement Albert was awarded the Cole Prize in algebra in 1939. Around 1942 Albert's research interests shifted from associative to nonassociative algebras. He wrote many important papers in this field. In 1965 Albert returned to his first love,structure theory of associative algebras.Most of Albert's important discoveries fall neatly into three categories: I. Associative Algebras, II. Riemann matrices, III. Nonassociative algebras.