Euclidean geometry (that's the one where we learn about area of shapes, sectors, etc.). Then you have the non-Euclidean geometries like elliptical geometry (Riemann geometry), which describes curved space.
What are the most widely accepted geometries of the universe?
I'm not sure what you mean by this. We have one current best-fit model for the spacetime geometry of the universe: it's an expanding universe with spatial slices of constant comoving time that are flat (Euclidean). The error bars in measurements still allow a small chance that the spatial geometry of slices of constant comoving time is a 3-sphere or an open "3-hyperbolic" geometry, either way with an extremely large radius of curvature (i.e., very close to flat). Is that what you're asking about?