Several kinds of finite poles and zeros are defined and their relationships are studied in an intrinsic manner. Some of these definitions are more precise than the usual ones (all kinds of multiplicities of an input-output decoupling zero are defined here). In addition, we believe that our approach clarifies those notions, and it makes it possible to very concisely establish fundamental relationships between various poles and zeros. Some new relationships are derived. The notions of input-output stability and transfer stability are also introduced. Several examples illustrate the theory.