B. We use the modal 'can' to make general statements about what is possible or allowed, or that somebody has the ability to do something: can + infinitive (can do/ can see etc.) (e.g. It can be very cold in winter. (= It is sometimes very cold in winter))
a. use 'could' as the past tense of 'can' (e.g. Listen. I can hear something. (now), I listened. I could hear something. (past)), we also use 'could' especially with: see, hear, small, taste, feel, remember, understand. (e.g. We had a lovely room in the hotel. We could see the lake.)
b. use 'could' to show that something is possible in the future, but not certain. (e.g. If we don’t hurry we could be late. (=Perhaps/Maybe we will be late))
c. also use 'could' to talk about possible actions now or in the future (especially to make suggestions) (e.g. A: What shall we do this evening? B: We could go to the cinema.) 'Can' is also possible in these sentences (e.g. We can go to the cinema. etc.) With 'could', the suggestion is less sure.
d. use 'could have' to show that something 'is/was' possible now or at some time in the past. (e.g. It’s ten o’clock. They could have arrived now.)
e. We use the negative 'can’t' or 'cannot' to show that something is impossible. (e.g. That can’t be true. You cannot be serious). We use 'couldn’t/could not' to talk about the past. (e.g. We knew it could not be true.)

B1. We use 'can' to talk about someone’s skill or general abilities. (e.g. She can speak several languages.) And use 'can' to talk about the ability to do something at a given time in the present or future (e.g. You can make a lot of money if you are lucky.)
a. also use 'could' to say that somebody had the general ability or permission to do something. (e.g. My grandfather could speak five languages.) And use 'could' to talk about past time (e.g. She could speak several languages.)
b. can say that somebody 'is able to' do something, but 'can' is more usual. (e.g. We are able to see the lake from our bedroom window.)
c. but ‘can’ has only two forms: 'can' (present) and 'could' (past). So sometimes it is necessary to use '(be) able to'. (e.g. I haven't been able to sleep recently.)
d. We use 'could' for general ability. But if you want to say that somebody did something in a specific situation, use 'was/ were able to' or 'managed to' (not could) (e.g. The fire spread through the building quickly, but fortunately everybody was able to escape/ managed to escape. (not could))
e. The negative 'couldn't (could not)' is possible in all situation. (e.g. My grandfather couldn't swim.)

B2. We use 'can' to ask for permission to do something. (e.g. Can I ask a question, please?)
a. 'could' is more formal and polite than 'can'. (e.g. Could I ask a question please? Could we go home now?)
b. use 'can' to give permission. (e.g. You can go home now if you like.) Also we use 'can' to say that someone has permission to do something. (e.g. We can go out whenever we want.)

B3. Instructions and requests: We use 'could' you and as a polite way of telling or asking someone to do something. (e.g. Could you take a message please?)
a. 'can' is less polite. (e.g. Can you take a message please?)

B4. Offers and invitations: We use 'can I ~' to make offers. (e.g. Can I help you?)
a. We sometimes say I can ~ or I could ~ to make an offer. (e.g. I can do that for you if you like.)