The paper describes methods of constructing of residually connected and flag-transitive geometries and corresponding presentations cf finite groups. The methods are illustrated on the finite simple group U4(2). As a result all residually connected and flag-transitive geometries of the group U4(2) with maximsl subgroups as the stabilizers of geometries' elements (exclsding rank 4 geometries with a trivial Borel subgroup) were described. USing these geometries several "natural" presentations of the group U4(2) were obtained.