According to the current view, the basic building blocks of matter are quarks and leptons, which interact with one another through the intermediaries of Yang-Mills gauge fields. The forms of interactions are determined by the algebraic structure of certain internal symmetry groups. The strong interactions are associated with the group SU(2) x U(1). This book is a concise introduction to the physical motivation behind these ideas and precise mathematical formulation thereof. The goal of this book is to explain why and how the mathematical formalism helps us to understand the relevant observed phenomena. This book serves as a text for a one-semester course beyond quantum field theory. The material was taken in part from such a course offered by the author at MIT.