Can is used to express ability in the present:

Can you lift the suitcase?

No, I can´t lift it.  It is very heavy.

  Could and was / were able to used for past ability: 

• was / were able to are used to speak about the ability a person had to do something in a particular situation. In the negative form you can use "could not" or  "was not / were not able":
   
  Jim was driving fast and crashed into a tree but he was able to get out of his car without help.
  

• Could is used to speak about the ability a person had to perform an action whenever he wanted: 
   
  When Paul was young, he could run very fast.  (He could perform the action expressed by "run" whenever he felt like it)

 
 be able to is used in all other tenses:  Robert has been able to drive for five years. Jane will soon be able to play chess well.

CAN used to express PERMISSION

  Can is used to express permission in the present: Son to father: Can I borrow your car? 

  Could and was / were allowed to used to express permission in the past:

• Could is used to express general permission:
   
  Margaret : When I was a girl, I could return home at eleven o´clock on Saturdays.
  
• Was / were allowed to are used to talk about permission in a particular situation:
   
  Tourist: I was allowed to get near the Queen.
   
  In the negative form the difference is not so clear-cut.

 be allowed to is used to form all other tenses: He will not be allowed to get back home at 5 a.m.