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This paper provides a detailed discussion with references on the fundamentals of the Analytic Hierarchy Process and in particular of relative measurement. The points discussed are grouped under the following categories: Structure in the AHP — Hierarchies and Networks, Scales of Measurement, Judgments, Consistency and the Eigenvector, Synthesis and Normative vs. Descriptive. The paper also includes a discussion of rank and a number of citations of rank reversals attributed to a variety of factors ranging from intransitivity to procedure invariance, that are thought to be unexplained by Utility Theory with its underlying principle to always preserve rank. It is shown that when there is synergy due to the number of elements the AHP can be used to both preserve rank when it is desired to preserve it and allow it to reverse when it should reverse.