Strip cabbage of its outer leaves; rinse the head well and pat dry.
 

Now slice the cabbage in half through its tough, fibrous core with a long, sturdy knife.

Cut each half in half again through the core. This will expose the core to make it easy to remove.

Holding each cabbage quarter upright, remove the tough core.

Now you can slice the cabbage into long, thin strips for slaws, salads, soups or stews or thicker strips for braises and sautés.