1. The incompressible equations in one horizontal dimension.
Equations in Eulerian coordinates.
Equations in Isopicnic coordinates.
Continuum limit of the N-layer equations.
The Montgomery variable.
2. Boundary Conditions.
3. Linearized stability theory. The Richardson number criteria.
4. Failure of the linearization at infinity.
5. Wave breaking and shock/hydraulic jump formation.
6. Single layer theory hydraulic jump conditions.
7. The effects of rotation on wave breaking.
9. Open problems in more than one layer.
The effects of mixing.
Lack of a complete theory for hydraulic jumps.
Partial closures for strong shocks in "one-and-a-half" layer theory