1 Motivation to study abstract algebra, binary operations, definition of a group

2 Elementary theorems, notation, order of an element

3 Subgroups, cyclic subgroups

4 Composition of functions as a binary operation, isometries of the plane

5 Symmetric group, alternating group

6 Isomorphism, homomorphism, direct products, classifying groups of (very!) small order

7 Definition of a ring, subring, ideal

8 The unit group of a ring, including Fermat's Little Theorem and Euler Totient function

9 Uniqueness of factorisation in polynomial ring F[x] where F is a field (irreducible polynomials, principal ideals). Covered Eisenstein's criterion for irreducibility over Q (given without proof)

10 Quotient rings and ring homomorphisms (including how to construct C as a quotient of R[x])