1. Introduction 2. Preliminaries 3. One parameter families 4. Weierstrass points, Porteous's formula, and $\bar {D}_{g-1,g-1}$ 5. A compactification of the Hurwitz scheme 6. Some enumerative problems 7. The class of $\bar {D}_{g-1,g-1}$ Appendix 1. Exceptional Weierstrass points of type $g+1$ Appendix 2. Weierstrass points on singular curves Appendix 3. Complete families of smooth curves of genus $3$
