Verbo modal CAN-COULD

Gramática

"Can" y "could" se utilizan para expresar permiso, posibilidad o habilidad. Como regla general "can" se utiliza en el presente y "could" en el pasado, pero hay ciertos matices:

a) Posibilidad / habilidad

En el presente "can" y en el pasado "could" o "was / were able".

With the new motorway you can go from Madrid to Barcelona in less than 4 hours

Ten years ago you could go from Madrid to Barcelona in 6 hours

I can play tennis

I could (was able) to play tennis when I was a child

"Could" también se utiliza con un sentido condicional, mientras que en el futuro se emplea "will be able":

If I had money I could buy a new car

In two years I will be able to speak English fluently

b) Permiso

En el presente distinguimos:

- Tener o pedir permiso: "can" tiene un sentido informal y "could" formal.

I can use the company's car for my private trips (informal)

I could use the company's car for my private trips (formal)

Can I borrow your car ? (informal)

Could I borrow your car ? (formal)

- Dar permiso: se utiliza "can"; "could" únicamente se emplea con un sentido condicional.

Tonight you can stay with us

If you don't find any other place, you could stay with

En el pasado se utiliza "could" y en el futuro "can".

c) Ofrecimiento

Sólo se utiliza "can".

Can I help you?

CAN/COULD Requests-Peticiones

Can/Could you give me a larger size, please?
Can/Could I have some stamps, please?
Can/Could you tell me the way to the station, please?
Could I use your telephone? (formal, polite)
Can I wear your green T-shirt today? (informal)
If Susan calls again, can you tell her to phone back later?
If Peter calls again, could you tell him I'm out?
Can/Could you ask her to phone me at work?

Fuente: http://www.aulafacil.com/Ingejerc/Lecciones/Lecc24.htm
              http://www.mujerpalabra.net/secundaria/pages/asignaturas/english/verbs_4/
             modals4eso.htm