  This Festschrift in honour of J. A. de Azcarraga gives an introduction to the
concept of duality, i.e., to the relativity of the notion of a quantum, in the
context of the quantum mechanics of a finite number of degrees of freedom.
Although the concept of duality arises in string and M--theory, Vafa has argued
that it should also have a counterpart in quantum mechanics, before moving on
to second quantisation, fields, strings and branes. We illustrate our analysis
with the case when classical phase space is complex projective space, but our
conclusions can be generalised to other complex, symplectic phase spaces, both
compact and noncompact.
