Introduction.- 1 Simple quadratic forms.- 2 Fermat''s Last Theorem.- 3 Lagrange''s theory of quadratic forms.- 4 Gauss''s Disquisitiones Arithmeticae.- 5 Cyclotomy.- 6 Two of Gauss''s proofs of quadratic reciprocity.- 7 Dirichlet''s Lectures.- 8 Is the quintic unsolvable?.- 9 The unsolvability of the quintic.- 10 Galois''s theory.- 11 After Galois - Introduction.- 12 Revision and first assignment.- 13 Jordan''s Trait- 14 Jordan and Klein.- 15 What is ''Galois theory''?.- 16 Algebraic number theory: cyclotomy.- 17 Dedekind''s first theory of ideals.- 18 Dedekind''s later theory of ideals.- 19 Quadratic forms and ideals.- 20 Kronecker''s algebraic number theory.- 21 Revision and second assignment.- 22 Algebra at the end of the 19th century.- 23 The concept of an abstract field.- 24 Ideal theory.- 25 Invariant theory.- 26 Hilbert''s Zahlbericht.- 27 The rise of modern algebra - group theory.- 28 Emmy Noether.- 29 From Weber to van der Waerden.- 30 Revision and final assignment.- A Polynom
