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 I change the color of the scroll bar?
Will I be allowed to reconfigure the seat of our network?
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.
Example:
He can add a hyperlink on the webpage.
Jane is able to get an include on every important webpage.
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.
Example:
John has been able to obtain an interlaced system.
Larry has been able to understand traffic shaping trends over the past few months.
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.
Example:
The server was able to connect to the internet last month.
Jenny was able to install her own upgrade.
'Could' and 'was / were able to' are also used to express a general ability in the past in the positive and negative forms.
Example:
The programmer was able to build a loop into any program.
He could install the SCSI cable whenever the system rebooted.