"Version: 20180501"--Title page verso.Includes bibliographical references.1. Introduction -- 2. Background and definitions -- 2.1. Classical mechanics -- 2.2. Quantum mechanics -- 2.3. Integrability and superintegrability3. Separation of variables -- 3.1. Some approaches to separability -- 3.2. The Levi-Civita procedure -- 3.3. Nonorthogonal separation : examples -- 3.4. Intrinsic characterizat…