F2 (also known as the 'spider-script') extends Blender native functionality of creating faces. It allows you to create a face from a single vertex selection or a single edge selection, while retaining all the built-in functionality.
Open Blender and go to Preferences then the Add-ons tab.
Click Mesh then F2 to enable the script.
Quad from Vertex
When a single vertex is selected, a new quad is formed by creating a new vertex. The position of this new vertex is calculated based on the three existing vertices. These are the selected vertex, and two vertices to which it is connected via open edges. An open edge is an edge which is only part of one face, or none at all. The newly created quad has the same material and normal direction as the neighboring faces.
Quad from Edge
Similar to the Quad from Vertex functionality, this is based on open edges. The selected edge has to be connected to two open edges. The vertices that belong to these edges are used to create a new quad.
If there are multiple ways to create a new quad, the position of the mouse cursor is taken into account. Of the multiple new faces which are possible, the one which will be closest to the mouse cursor (in 2D screen space) is the one which will be created.
Extends the 'Make Edge/Face' functionality.
Mesh Edit Mode F
Bart Crouch, Alexander Nedovizin, Paul Kotelevets (concept design), Adrian Rutkowski
This add-on is bundled with Blender.