The modal auxiliary can is used
- to express ability (in the sense of being able to do something or knowing how to do something):
He can speak Spanish but he can't write it very well. - to expression permission (in the sense of being allowed or permitted to do something):
Can I talk to my friends in the library waiting room? (Note that can is less formal than may. Also, some writers will object to the use of can in this context.) - to express theoretical possibility:
American automobile makers can make better cars if they think there's a profit in it.
The modal auxiliary could is used
- to express an ability in the past:
I could always beat you at tennis when we were kids. - to express past or future permission:
Could I bury my cat in your back yard? - to express present possibility:
We could always spend the afternoon just sitting around talking. - to express possibility or ability in contingent circumstances:
If he studied harder, he could pass this course.
In expressing ability, can and could frequently also imply willingness: Can you help me with my homework?