Linear Groups: With An Exposition Of The Galois Field Theory (1901) by Leonard Eugene Dickson is a comprehensive book that explores the theory of linear groups and Galois field theory. The book is divided into two parts. The first part deals with the theory of linear groups, including their definition, properties, and various examples. The second part of the book focuses on Galois field theory, which is a branch of abstract algebra that deals with the study of finite fields.The book begins with an introduction to linear groups and their properties, including the concept of a group, subgroups, and homomorphisms. It then goes on to explore the theory of linear transformations, including the concept of an invariant subspace and the Jordan canonical form. The book also covers the theory of finite groups, including the classification of finite simple groups.In the second part of the book, Dickson introduces the concept of a Galois field, which is a finite field with a characteristic prime number. He then goes on to explore the properties of Galois fields, including their structure, subfields, and automorphisms. The book also covers the theory of Galois extensions, including the Galois correspondence and the fundamental theorem of Galois theory.Overall, Linear Groups: With An Exposition Of The Galois Field Theory (1901) is an essential resource for anyone interested in the theory of linear groups and Galois field theory. It is written in a clear and concise style, making it accessible to both students and researchers in the field of abstract algebra.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.