This is the first volume of a revised edition of P.M. Cohn's classic three-volume text Algebra, widely regarded as one of the most outstanding introductory algebra textbooks. This volume covers the important results of algebra. Readers should have some knowledge of linear algebra, groups and fields, although all the essential facts and definitions are recalled.

1. Sets.- 2. Groups.- 3. Lattices and Categories.- 4. Rings and Modules.- 5. Algebras.- 6. Multilinear Algebra.- 7. Field Theory.- 8. Quadratic Forms and Ordered Fields.- 9. Valuation Theory.- 10. Commutative Rings.- 11. Infinite Field Extensions.- List of Notations.- Author Index.