Part One The Basic Objects o Aebra Chapter I Groups 1. Monoids 2. Groups 3. Normal subgroups 4. Cyclic groups 5. Oraios of a group on a set 6. Sylow subgroups 7. Direct sums and free abelian groups 8. Finitely generated abelian groups 9. The dual group 10. Inverse limindcmlio 11. Categories and functors 12. Free groups Chapter II Rings 1. Rings and homomorphisms 2. Commutative rings 3. Polynomials and group rings 4. Localization 5. Principal and factorial rings Chapter III Modules 1. Basic definitions 2. The group of homomorphisms 3. Direct products and sums of modules 4. Free modules 5. Vector spaces 6. The dual space and dual module 7. Modules over principal rings 8. Euler-Poincare maps 9. The snake lemma 10. Direct and inverse limits Chapter IV Polynomials 1. Basic properties for polynomials in one variable 2. Polynomials over a factorial ring 3. Criteria for irreducibility 4. Hilbert's theorem 5. Partial fractions 6. Symmetric polynomials 7. Mason-Stothers theorem and the abe conjecture 8. The resultant 9. Power series Part Two Algebraic Equations Chapter V Algebraic Extensions 1. Finite and algebraic extensions 2. Algebraic closure 3. Splitting fields and normal extensions 4. Separable extensions 5. Finite fields 6. Inseparable extensions Chapter VI Galois Theory