Introduction  
1. Setting the Scene  
2. Singularity Loci of the Theta Divisor  
3. Loci in $\mathcal{A}_{g}$ Defined by Singularities of the Theta Divisor  
4. Compactifications of $\mathcal{A}_{g}$  
5. Class Computations, and Intersection Theory on $\mathcal{X}_{g}$  
6. Degeneration: Technique and Results