Speaking about Abilities
Can - Be Allowed to
'Can' is used to ask for and give permission. In the simplest sense, we use 'can' to request something. However, at other times 'can' expresses permission to do something specific. 'May' is also used in a more formal sense. In American English, 'May I ...' is considered the correct formal form to ask for permission.
'To be allowed to' can also be used to ask for and give permission. This form is more formal and is commonly used for rules and regulations.
Examples of Asking Permission
Can we ask you for the forms we need to start an international NGO?
Are they able to explain the purpose of effective investigation and documentation of torture?
Can - To Be Able To
'Can' is commonly used to express the ability to do something. This usage is similar to the form 'to be able to do something'. Both these forms are acceptable, although 'can' is more commonly used.
Quasi-autonomous non-governmental organizations can lead the environmental movement.
Jon is able to explain the effects of racism.
To Be Able To - Future and Perfect Forms
There is no future or perfect form of 'can'. Use 'to be able to' in all future and perfect tenses.
Terry Gilliam has been able to research the subject for his film.
Remote viewers have been able to employ new techniques of knowledge management.
Special Case of the Past Positive
Use 'was / were able to' when speaking about a specific event in the past in the positive form. Both 'can' and 'to be able to' are used in the past negative to speak about specific events.
Jenny was able to explain the issues during her presentation.
The NGO was able to find the key influencer during the survey.
'Could' and 'was / were able to' are also used to express a general ability in the past in the positive and negative forms.
Bob was able to bring local action to bear on international issues when he was a community organizer.
The salesman could always meet his quota.