Sol geometry is one of the eight homogeneous Thurston 3-geometriesIn [13] the densest lattice-like translation ball packings to a type (type I/1 in this paper) of Sol lattices has been determined. Some basic concept of Sol were defined by P. SCOTT in [10], in general.In our present work we shall classify Sol lattices in an algorithmic way into 17 (seventeen) types, in analogy of the 14 Bravais types of the Euclidean 3-lattices, but infinitely many Sol affine equivalence classes, in each type. Then the discrete isometry groups of compact fundamental domain (crystallographic groups) can also be classified into infinitely many classes * Mathematics Subject Classification 2010: 22E25, 22E40, 57M60, 53A35.