To move an object slowly and carefully in a particular direction.

“He edged the book across the table.”

To move slowly and carefully in a particular direction.

“He edged away from her.”

(usually in the form 'just edge') To win by a small margin.

That has a sharp planar surface.

“The monks were forbidden to carry edged weapons such as swords and axes.”

Followed by with: Having an edging of a certain material, color, and so on.

“a coat edged with fur”