**1. The incompressible equations in one horizontal dimension.**

Equations in Eulerian coordinates.

Equations in Isopicnic coordinates.

N-layer equations.

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