Could is a modal auxiliary verb. There is no –s in the third person singular.

Could is used to indicate ability that existed in the past. It is followed by an infinitive without to.

• In my younger days I could run four miles at a stretch.
• Till last year I could read without glasses.

Questions and negatives are made without do.

• Could I have a word with you?
• Why couldn't you attend the meeting yesterday?
• We found that we couldn't depend on our guide.

Uses

To talk about past ability in general

Could is often used to say that somebody was able to do something in the past.

• • My father could walk without help when he was 95.
  • She could read when she was 3.
  • When we were children, we could watch TV whenever we wanted to.
  • In my younger days, I could run four miles at a stretch.

Note that could refers to the past only when the context makes the time clear.

Could not (also couldn't) shows past inability.

• I could not understand a word, but I kept smiling.
• She spoke in such a low voice that most of us could not hear her.
• We found that we couldn't depend on our guide.

Could is used to talk about past ability in general. We do not normally use could to say that somebody managed to do something on one occasion. But with certain verbs like see, hear, taste, feel, smell, understand, remember etc., could can be used for particular occasions as well.

• Suddenly I could hear a loud noise.
• I could smell something burning.

As the past equivalent of can

Could is the past equivalent of can in indirect speech.

• He said, "I can drive."
• He said that he could drive.
• She said, "I can't climb up the hill."
• She said that she could not climb up the hill.

To make polite requests or offers

Could is often used to make a request or offer sound more polite.

• Could I have a glass of water, please?
• Could you help me with these bags?

To express possibility or uncertainty

Could can mean would be able to.

• You could get a better job if you spoke English. (=You would be able to get a better job if you spoke English.)
• You could do it if you tried hard. (=You would be able to do it…)
• If only I had some working capital, I could start a new business. (=…I would be able to start a new business.)

Could have + past participle

The structure could have + past participle can be used to criticize people for not doing things. It can also be used to talk about past events that did not happen.

• I have been waiting since morning - you could have said that you weren't coming.
• Why did you drive so carelessly? You could have killed yourself.