The present volume is the first of three that will be published under the general title Lectures in lbstract fllgebra. These vol-umes are based on lectures which the author has given during the past ten years at the University of North Carolina, at The Johns Hopkins University, and at Yale University. The general plan of the work is as follows.The present first volume gives an introduction to abstract algebra and gives an account of most of the important algebraic concepts. In a treatment of thi

INTRODUCTION￡oCONCEPTS FROM SET THEORY
THE SYSTEM OF NATURAL NUMBERS
SECTION
1. Operations on sets
2. Product sets, mappings
3. Equivalence relations
4. The natural numbers
5. The system of integers
6. The division process in I
CHAPTER I￡oSEMI-GROUPS AND GROUPS
1 ￡?Definition and examples of semi-groups
2. Non-associative binary compositions
3. Generalized associative law. Powers
4. Commutativity
5. Identities and inverses
6. Definition and examples of groups
7. Subgroups
8. Isomorphism
9. Transformation groups
10. Realization of a group as a transformation group
11. Cyclic groups. Order of an element
12. Elementary properties of permutations
13. Coset decompositions of a group
14. Invariant subgroups and factor groups
15. Homomorphism of groups
16. The fundamental theorem of homomorphism for groups
17. Endomorphisms, automorphisms, center of a group
18. Conjugate classes
……