  We give an enumeration of all positive definite primitive Z-lattices in
dimension >= 3 whose genus consists of a single isometry class. This is
achieved by using bounds obtained from the Smith-Minkowski-Siegel mass formula
to computationally construct the square-free determinant lattices with this
property, and then repeatedly calculating pre-images under a mapping first
introduced by G. L. Watson. We hereby complete the classification of
single-class genera in dimensions 4 and 5 and correct some mistakes in Watson's
classifications in other dimensions. A list of all single-class primitive
Z-lattices has been compiled and incorporated into the Catalogue of Lattices.
