Aims The aim of this book is to provide a guide to arich and fascinatings- ject: algebraic curves, and how they vary in families. The revolution that the ?eld of algebraic geometry has undergone with the introd- tion of schemes, together with new ideas, techniques and viewpoints introduced by Mumford and others, have made it possible for us to understand the behavior of curves in ways that simply were not pos- ble a half-century ago.