This book is an introduction to integrability and conformal field theory in two dimensions using quantum groups. The book begins with a brief introduction to S-matrices, spin chains and vertex models as a prelude to the study of Yang-Baxter algebras and the Bethe ansatz. The authors then introduce the basic ideas of integrable systems, giving particular emphasis to vertex and face models. They give special attention to the underlying mathematical tools, including braid groups, knot invariants, and towers of algebras. The authors then go on to give a detailed introduction to quantum groups before addressing integrable models, two-dimensional conformal field theories, and superconformal field theories. The book contains many diagrams and exercises to illustrate key points in the text and will be appropriate for researchers and graduate students in theoretical physics and mathematics.