The present volume is the first of three that will be published under the general title Lectures ilbstract fllgebra. These vol-umes are based olectures which the author has giveduring the past teyears at the University of North Carolina， at The Johns Hopkins University， and at Yale University. The general plaof the work is as follows.The present first volume gives aintroductioto abstract algebra and gives aaccount of most of the important algebraic concepts. Ia treatment of this type it is impossible to give a comprehensive account of the topics which are introduced. Nevertheless we have tried to go beyond ?the foundations and elementary properties of the algebraic sys-tems. This has necessitated a certaiamount of selectioand omission. We feel that eveat the present stage a deeper under-standing of a few topics is to be preferred to a superficial under-standing of many.