Summary: In the framework of geometric quantization we explicitly construct, in a uniform fashion, a unitary minimal representation \(\pi_ 0\) of every simply-connected real Lie group \(G_ 0\) such that the maximal compact subgroup of \(G_ 0\) has finite center and \(G_ 0\) admits some minimal representation. We obtain algebraic and analytic results about \(\pi_ 0\). We give several results on the algebraic and symplectic geometry of the minimal nilpotent orbits and then “quantize” these results to obtain the corresponding representations. We assume \((\text{Lie }G_ 0)_ \mathbb{C}\) is simple.