Mathematics is playing an increasingly important role in society and the sciences, enhancing our ability to use models and handle data. Applied Mathematics: A Very Short Introduction introduces the field of applied mathematics and explores its relationships with pure mathematics, science, and engineering. Explaining the nature of applied mathematics, it discusses its early achievements in physics and engineering, and its development as a separate field after World War II. Using historical examples, current applications, and challenges, this VSI illustrates the particular role that mathematics plays in the modern sciences today and its far-reaching potential.