Classical algebra: its nature, origins, and uses

pt. 1. Numbers and equations. What algebra is

Equations and their solutions

Where algebra comes from

Why algebra is important

Numerical solution of equations

pt. 2. The formulaic approach to equations. Combinatoric solutions I: quadratic equations

Combinatoric solutions II: cubic equations

pt. 3. Resolvents. From combinatorics to resolvents

The search for resolvents

pt. 4. Abstract algebra. Existence and constructibility of roots

The breakthrough: Galois Theory

Modern Algebra / Roger Cooke.