Electronic and geometrical structures of Mn-3-Mn-10 together with their singly negatively and positively charged ions are computed using density functional theory with generalized gradient approximation. The ground-state spin multiplicities in the neutral series are 16, 21, 4, 9, 6, 5, 2, and 5, for Mn-3-Mn-10, respectively. Thus, there is a transition from a ferromagnetic ground state to a ferrimagnetic ground state at Mn-5. The energy difference between ferrimagnetic and ferromagnetic states in Mn-n grows rapidly with increasing n and exceeds 2 eV in Mn-10. The corresponding change from ferro- to ferrimagnetic ground state occurs at Mn-6(-) and Mn-3(+) in the anionic and cationic series, respectively. Beginning with Mn-6, the ion spin multiplicities differ from that of the neutral by +/- 1 (i.e., they obey the empirical "+/- 1 rule"). We found that the energy required to remove an Mn atom is nearly independent of the charge state of an Mnn cluster and the number of atoms in the cluster, except for Mn-3. The results of our calculations are in reasonable agreement with experiment, except for the experimental data on the magnetic moments per atom, where, in general, we predict smaller values than the experiment.