  We introduce the concept of an $E$-valued function algebra, a type of Banach
algebra that consist of continuous $E$-valued functions on some compact
Hausdorff space, where $E$ is a Banach algebra. We present some basic results
about such algebras, having to do with the Shilov boundary and the set of peak
points of some commutative $E$-valued function algebras. We give some specific
examples.
