These are lecture notes (arXiv:2309.17369) for an introductory course on noncommutative field and gauge theory. We begin by reviewing quantum mechanics as the prototypical noncommutative theory, as well as the geometrical language of standard gauge theory. Then, we review a specific approach to noncommutative field and gauge theory, which relies on the introduction of a derivations-based differential calculus. We focus on the cases of constant and linear noncommutativity, e.g., the Moyal spacetime and the so-called ℝ3λ, respectively. In particular, we review the gφ4 scalar field theory and the U(1) gauge theory on such noncommutative spaces. Finally, we discuss noncommutative spacetime symmetries from both the observer and particle point of view. In this context, the twist approach is reviewed and the λ-Minkowski gφ4 model is discussed.