Using Boolean modifiers to cut holes in objects

Booleans are a 3D extension of the Venn diagrams taught in an algebra class. Named after George Boole, Boolean is pronounced "Bool-ee-in" with emphasis on "Bool". Bool rhymes with tool.

There are three kinds of Boolean operators: Difference, Intersection, and Union. The following figure shows that the circle A represents the object to which you add the Boolean modifier and the circle B represents the object added by the Boolean modifier.

The Difference operation leaves all of object A that is not part of object B. With the Intersection operation, only what is common to both objects A and B is left. The Union operation combines the two objects.