These are the lecture notes of a one-semester undergraduate course which we have taught several times at Binghamton University (SUNY) and San Francisco State University. For many of our students, complex analysis is their first rigorous analysis (if not mathematics) class they take, and these notes reflect this very much. We tried to rely on as few concepts from real analysis as possible. In particular, series and sequences are treated “from scratch.” This also has the (maybe disadvantageous) consequence that power series are introduced very late in the course.
We thank our students who made many suggestions for and found errors in the text. Special thanks go to Collin Bleak, Jon Clauss, Sharma Pallekonda, and Joshua Palmatier for comments after teaching from this book.