  This article points out that observables and instruments can be combined in
many ways that have natural and physical interpretations. We shall mainly
concentrate on the mathematical properties of these combinations. Section~1
reviews the basic definitions and observables are considered in Section~2. We
study parts of observables, post-processing, generalized convex combinations,
sequential products and tensor products. These combinations are extended to
instruments in Section~3. We consider properties of observables measured by
combinations of instruments. We introduce four special types of instruments,
namely Kraus, L\"uders, trivial and semitrivial instruments. We study when
these types are closed under various combinations. In this work, we only
consider finite-dimensional quantum systems. A few of the results presented
here have appeared in the author's previous articles.
