Group theory is one of the most fundamental branches ofmathematics. This volume of the Encyclopaedia is devoted totwo important subjects within group theory. The first partof the book is concerned with infinite groups. The authorsdeal with combinatorial group theory, free constructionsthrough group actions on trees, algorithmic problems, periodic groups and the Burnside problem, and the structuretheory for Abelian, soluble and nilpotent groups. They haveincluded the very latest developments; however, the materialis accessible to readers familiar with the basic concepts ofalgebra. The second part treats the theory of linear groups. It is agenuinely encyclopaedic survey written for non-specialists. The topics covered includethe classical groups, algebraicgroups, topological methods, conjugacy theorems, and finitelinear groups. This book will be very useful to allmathematicians, physicists and other scientists including graduate studentswho use group theory in their work.