Book excerpt: This book contains papers presented at the Second International Conference on Algebra, held in Barnaul in August 1991 in honour of the memory of A. I. Shirshov (1921--1981). Many of the results presented here have not been published elsewhere in the literature. The collection provides a panorama of current research in PI-, associative, Lie, and Jordan algebras and discusses the interrelations of these areas with geometry and physics. Other topics in group theory and homological algebra are also covered.