  This article considers quantum systems described by a finite-dimensional
complex Hilbert space $H$. We first define the concept of a finite observable
on $H$. We then discuss ways of combining observables in terms of convex
combinations, post-processing and sequential products. We also define
complementary and coexistent observables. We then introduce finite instruments
and their related compatible observables. The previous combinations and
relations for observables are extended to instruments and their properties are
compared. We present four types of instruments; namely, identity, trivial,
L\"uders and Kraus instruments. These types are used to illustrate different
ways that instruments can act. We next consider joint probabilities for
observables and instruments. The article concludes with a discussion of
measurement models and the instruments they measure.
