This book has grown from my courses on Category Theory at Carnegie Mellon University over the last ten years. In that time, I have given numerous lecture courses and advanced seminars to undergraduate and graduate students in Computer Science, Mathematics, and Logic. The lecture course based on the material in this book consists of two, 90-minute lectures a week for 15 weeks. The germ of these lectures was my own graduate student notes from a course on Category Theory given by Mac Lane at the University of Chicago. In teaching my own course, I soon discovered that the mixed group of students at Carnegie Mellon had very different needs than the Mathematics graduate students at Chicago, and my search for a suitable textbook to meet these needs revealed a serious gap in the literature. My lecture notes evolved over time to fill this gap, supplementing and eventually replacing the various texts I tried using.