Mortar finite elements are nonconforming finite elements that allow for a geometrically nonconforming decomposition of the computational domain and, at the same time, for the optimal coupling of different variational approximations in different subregions. Poincare and Friedrichs inequalities for mortar finite elements are derived. Using these inequalities, it is shown that the condition number for self-adjoint elliptic problems discretized using mortars is comparable to that of the conforming finite element case. Geometrically non-conforming mortars of the second generation are considered, i.e. no continuity conditions are imposed at the vertices of the subregions.