This is a book of "impressions" of a journey through the theory of com-
plex algebraic curves. It is neither self-contained, balanced, nor
particularly tightly organized. As with any notebook made on a journey,
what appears is that which strikes the writer's fancy. Some topics
appear because of their compelling intrinsic beauty. Others are left out
because, for all their impor- tance, the traveler found them boring or
was too dull or lazy to give them their due. Looking back at the end of
the journey, one can see that a common theme in fact does emerge, as is
so often the case; that theme is the theory of theta functions. In fact
very much of the material in the book is prepara- tion for our study of
the final topic, the so-called Schottky problem. More than once, in
fact, we tear ourselves away from interesting topics leading elsewhere
and return to our main route.