We have been working on this project for over ten years, and at times we have felt that we have only brought on ourselves a plague of locus. However, our spirits have been lightened, and the project made far easier and more successful than it would have been, by the interest and help of many people.

First of all, we thank Bill Fulton, who created much of the modern approach to intersection theory, and who directly informed our view of the subject from the beginning.

Many people have helped us by reading early versions of the text and providing comments and corrections. Foremost among these is Paolo Aluffi, who gave extensive and detailed comments; we also benefited greatly from the advice of Francesco Cavazzani and Izzet CoŞkun. We would also thank Mike Roth and Stephanie Yang, who provided notes on the early iterations of a course on which much of this text is based, as well as students who contributed corrections, including Sitan Chen, Jun Hou Fung, Changho Han, Chi-Yun Hsu, Hannah Larson, Ravi Jagadeesan, Aaron Landesman, Yogesh More, Arpon Raksit, Ashvin Swaminathan, Arnav Tripathy, Isabel Vogt and Lynnelle Ye.

Silvio Levy made many of the many illustrations in this book (and occasionally corrected our mathematical errors too!). Devlin Mallory then took over as copyeditor, and completed the rest of the figures. We are grateful to both of them for their many improvements to this text (and to Cambridge University Press for hiring Devlin!).

We are all familiar with the after-the-fact tone—weary, self-justificatory, aggrieved, apologetic— shared by ship captains appearing before boards of inquiry to explain how they came to run their vessels aground, and by authors composing forewords.