Window > Pathfinder
You use the Pathfinder panel 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.
The bottom row of buttons in the panel, called pathfinder effects, let you create final shape combinations on the first click. Pathfinder effects let you create new shapes out of overlapping objects.
To create the shape below:
Open a new document in Illustrator.
Draw a rectangle.
Draw a small circle:
Option (Alt) drag the circle to the right. It will duplicate and move the circle.
To repeat the last action, use Command (Ctrl) D
Duplicate the circles few more times.
Select all circles and align them using Align panel (Window > Align)
Select the rectangle and the circles:
In Pathfinder panel: click on Subtract button:
This will remove all shape properties (color and stroke, but leaves the paths):
Click on Expand button (it will remove the paths too):
The top part of the shape is done:
For the bottom part:
Draw a small rectangle.
In Transform palette (Window > Transform) change Shear option to 10:
Duplicate the small rectangle by Option (Alt) dragging it
Command (Ctrl) D to add more rectangles:
Select all small rectangles.
Align them with Align panel (there is also a "Distribute evenly" option that you can use):
Select all shapes.
Click on Subtract button in Pathfinder panel:
Draw a rectangle:
Draw another rectangle (or square):
Add three tiny rectangles, select the following four shapes:
Click Subtract button in Pathfinder panel:
Duplicate the left shape by Option (Alt) dragging it:
Object > Transform > Reflect:
Select all three shapes:
In Pathfinder panel - click Add button. Expand.
Now you need to recreate the two shapes below using the Pathfinder palette: