Topology

Point set topology

1. ★★★★★ Topology I: limits, morphisms, the neighbourhood filter, open sets
2. ★★★★☆ Topology II: Kuratowski closure topology, nets, neighbourhood basis, dense sets
3. ★★★★☆ Topology III: example topologies, inherited topologies, distinguishability 
4. ★★★★☆ Supplementary definitions: connectedness, clopen sets
5. ★★★★☆ Supplementary definitions: compactness, compactification, hemicompactness
6. Supplementary definitions: local stuff
7. ★★★★☆ Supplementary definitions: levels of abstraction
8. Supplementary definitions: paracompactness -- see, see, see
9. Wrapping, unwrapping and simply connectedness
10. Topology of Euclidean space, etc. -- see, see
11. Metrisability -- see, see?
12. Knot theory

Algebraic topology

1. Paths, dimensions, Fundamental group, contractibility, homotopy, topological invariants, etc.
2. Euler characteristic, etc.

Homology, Cohomology, Topology of derivatives and Stokes' theorem [1]