You use the Pathfinder panel (Window > Pathfinder) to combine objects into new shapes.

The top row of buttons in the panel, called shape modes, let you control the interaction between components of a compound shape. You can choose from the following shape modes:

Add To Shape Area

Adds the area of the component to the underlying geometry.

Subtract from Shape Area

Cuts out the area of the component from the underlying geometry.

Intersect Shape Areas

Uses the area of the component to clip the underlying geometry as a mask would.

Exclude Overlapping Shape Areas

Uses the area of the component to invert the underlying geometry, turning filled regions into holes and vice versa.

Shape modes

A.

All components in Add mode

B.

Subtract mode applied to squares

C.

Intersect mode applied to squares

D.

Exclude mode applied to squares

The bottom row of buttons in the panel, called pathfinder effects, let you create final shape combinations on the first click. (See Apply Pathfinder effects.)