Curious Curves is self-contained and unified in presentation. This book is suitable for a topics course, capstone course, or senior seminar; it is also intended for independent study by students and others interested in mathematics.Curves can often provide a better representation of natural phenomena than do the figures of classical geometry. Thus the content -- presented with an emphasis on the geometric intuition characteristic of the study of curves -- is highly relevant not only for people working in mathematics, but also those in other sciences. The explanations are detailed and illustrative to capture the interest of the reader, as well as complete to provide the necessary background information needed to go further into the subject.