A gyroviscous model of the magnetopause current layer is applied to the entire magnetopause with the inner boundary condition provided by a quantitative model of the magnetospheric field (BM) and the outer boundary condition given by the interplanetay magnetic field (IMF) draped against the magnetopause surface. It is found that the magnetopause surface is divided into at least four different regions by a tangential singularity line (Bn=0) that separates regions with different signs of the normal component and rotation singularity lines (BM∥BIMF) that separate regions with different magnetic polarization (rotations). The tangential singularity line (TSL) has topological properties similar to the classical reconnection line and the rotation singularity lines (RSL) are similar to lines of ''antiparallel merging.'' The field topology in the regular regions is determined by field line tracing using the model solutions. It is argued that the whole magnetopause surface, except the singular separation regions, possesses a stable rotational structure that can be described locally by a planar model. It is proposed that the singular regions on the magnetopause surface (TSL and RSL) play the role of gates for solar wind plasma entry into the magnetosphere and that rotational singularities are observed as flux transfer events. Observations of velocity jumps at the magnetopause that were previously classified as ''high-speed reconnection flows,'' ''tangential discontinuity'' crossings as well as ''diffusive entry'' crossings can all be explained as special cases of the gyroviscous merging theory. The paper offers a unified view of such disparate concepts as steady state reconnection, antiparallel merging, viscous interactions, patchy reconnection, flux transfer events, and impulsive penetration. ¿ American Geophysical Union 1991