The fundamental concepts of category theory are explained in this text which allows the reader to develop their understanding gradually. With over 300 exercises, students are encouraged to monitor their progression. A wide coverage of topics in category theory and computer science is developed including introductory treatments of cartesian closed categories, sketches and elementary categorical model theory, and triples. The presentation is informal with proofs included only when they are instructive, providing a broad coverage of the competing texts on category theory in computer science.