Writing for fellow professional mathematicians, Hazewinkel, Nadiya Gubareni, and V. V. Kirichenko focus mostly on Hopf algebras, though the first chapter is a fairly standard concise treatment of the established parts of Lie algebras, with a bit more emphasis than usual on Dynkin diagrams. Another seven chapters look at Hopf algebras from such perspectives as symmetric functions, noncommutative symmetric functions and quasi-symmetric functions, permutations, and applications and interrelation with other parts of mathematics and physics. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)