This is the first volume of the book Algebra planned by the authors to provide adequate preparation in algebra to prospective teachers and researchers in mathematics and related areas. Beginning with groups of symmetries of plane configurations, it studies groups (with operators) and their homomorphisms, presentations of groups by generators and relations, direct and semidirect products, Sylow’s theorems, soluble, nilpotent and Abelian groups. The volume ends with Jordan’s classification of finite subgroups of the group of orthogonal transformations of R3. An attractive feature of the book is its richness in purposeful examples and instructive exercises with a focus on the roots of algebra in number theory, geometry and theory of equations.

Preface / Notations / Preliminaries / Groups of Plane Symmetries / Groups and Their Homomorphisms / Subgroups, Normal Subgroups and Quotient Groups / Homomorphism Theorems / Direct and Semidirect Products / Finite Groups / Series of Subgroups/ Abelian Groups / Finite Subgroups of Orthogonal Groups/ Bibliography / Index

Undergraduate students, Prospective Teachers and Researchers