Non-Abelian phenomena on D-branes

A remarkable feature of D-branes is the appearance of a non-Abelian gauge theory in the description of several (nearly) coincident branes. This nonAbelian structure plays an important role in realizing various geometric effects with D-branes. In particular, the branesʹ transverse displacements are described by matrix-valued scalar fields and so noncommutative geometry naturally appears in this framework. I review the action governing this non-Abelian theory, as well as various related physical phenomena such as the dielectric effect, giant gravitons and fuzzy funnels.