Can

Modal auxiliary verbs may sound difficult but in fact they're easy. They are invariable (no conjugation). And the main verb is always the "bare infinitive" (the infinitive without "to").But Can and could are modal auxiliary verbs.Whereas be able to is NOT an auxiliary verb (it uses the verb be as a main verb). We include be able to here for convenience.
"Can" is one of the most commonly used modal verbs in English. It can be used to express ability or opportunity, to request or offer permission, and to show possibility or impossibility.
Can
They can control their own budgets. Ability / Possibility

We can’t fix it. Inability / Impossibility

Can I smoke here? Asking for permission

Can you help me? Request

Examples:

* I can ride a horse. ability
* We can stay with my brother when we are in Paris. opportunity
* She cannot stay out after 10 PM. permission
* Can you hand me the stapler? request
* Any child can grow up to be president. possibility

Using "Can" in Present, Past, and Future

Most modal verbs behave quite irregularly in the past and the future. Study the chart below to learn how "can" behaves in different contexts.
Modal Use Positive Forms
1. = Present 2. = Past 3. = Future Negative Forms
1. = Present 2. = Past 3. = Future You can also use:
can
general ability 1. I can speak Chinese.

2. SHIFT TO "COULD"
I could speak Chinese when I was a kid.

3. SHIFT TO "BE ABLE TO"
I will be able to speak Chinese by the time I finish my course.
1. I can't speak Swahili.

2. SHIFT TO "COULD"
I couldn't speak Swahili.

3. SHIFT TO "BE ABLE TO"
I won't be able to speak Swahili.
be able to
can
ability during a specific event 1. With a burst of adrenaline, people can pick up cars.

2. SHIFT TO "BE ABLE TO"
With a sudden burst of adrenaline, he was able to lift the car off the child's leg.

3. SHIFT TO "BE ABLE TO"
With a sudden burst of adrenaline, he will be able to lift the car.
1. Even with a burst of adrenaline, people can't pick up something that heavy.

2. SHIFT TO "BE ABLE TO"
Even the weight lifter, couldn't lift the car off the child's leg.

3. SHIFT TO "BE ABLE TO"
Even three men working together won't be able to lift the car.
be able to
can
opportunity 1. I have some free time. I can help her now.

2. SHIFT TO "BE ABLE TO"
I had some free time yesterday. I was able to help her at that time.

3. I'll have some free time tomorrow. I can help her then.
1. I don't have any time. I can't help her now.

2. SHIFT TO "BE ABLE TO"
I didn't have time yesterday. I wasn't able to help her at that time.

3. I won't have any time later. I can't help her then.
be able to
can
permission 1. I can drive Susan's car when she is out of town.

2. SHIFT TO "BE ALLOWED TO "
I was allowed to drive Susan's car while she was out of town last week.

3. I can drive Susan's car while she is out of town next week.
1. I can't drive Susan's car when she is out of town.

2. SHIFT TO "BE ALLOWED TO "
I wasn't allowed to drive Susan's car while she was out of town last week.

3. I can't drive Susan's car while she is out of town next week.
may
can
request Can I have a glass of water?

Can you give me a lift to school?

Requests usually refer to the near future.
Can't I have a glass of water?

Can't you give me a lift to school?

Requests usually refer to the near future.
could, may
can
possibility, impossibility Anyone can become rich and famous if they know the right people.

Learning a language can be a real challenge.

This use is usually a generalization or a supposition.
It can't cost more than a dollar or two.

You can't be 45! I thought you were about 18 years old.

This use is usually a generalization or a supposition.
could