A2M (‘Analysis to Mineralogy’) is a computer program to determine, for given total chemical analyses, all possible mineral modes from an arbitrary but pre-specified set of minerals. A2M is specifically designed to address the case in which the number of minerals is greater than the number of analysed elements (oxides). Since in this case the solution is not unique, all extreme mineral modes are determined. They span a finite convex polyhedron in the solution space with dimension ‘number of minerals’ minus ‘number of elements’. Every possible solution can be obtained as linear combination of the extreme modes; and the arithmetic mean of all extreme modes (i.e. the centre of gravity of the solution polyhedron) is a routine output of A2M, which can be regarded as the ‘best’ solution in the absence of any additional information. The use of A2M is illustrated with several examples.