can	current ability
could	past ability
can could	decisions made now about future ability
will be able to	future ability
could	current or general hypothetical ability
could	future hypothetical ability
could have	past hypothetical ability
cannot	the exception-word of the full negative forms of modals written as two words (a single word)
can could	the words which cannot be used as infinitves
to be able to	to phrase we use as infinitive instead CAN and COULD
was/were able to, managed to, succeeded, etc.	the words be used for past ability on one accasion
see, hear, feel, etc.	the verbs, with which we can use COULD for past ability on one accasion
may, could, can	asking for permission
may, may not, could, can	giving or refusing permission
was/were allowed to	verb which we use to talk about past permission
Hadn't you better check that these facts are actually true ?	Czy nie powinieneś był sprawdzić czy te fakty są właściwie prawdziwe ?
might, may	by these verbs we can give sugesstions, that are not perfect, but there is no better option
should have, ought to have, oughtn't to have	criticising past behaviour
could have, might have	expressing annoyance at past behaviour
will	criticising general behaviour
would	criticising a specific example of someone's general behaviour
must, mustn't, have (got) to, need (to)	current or general obligation
don't have to, haven't got to, needn't, don't need (to)	a lack of current or general obligation
will have to, must, mustn't, have (got) to, (will) need (to)	future obligation
don't have to, won't have to, haven't got to, needn't, don't need to, won't need to	a lack of future obligation
had to, needed (to)	past obligation
didn't have to, didn't need (to), needn't have	a lack of past obligation
must	the verb we use for personal obligation
have to	the verb we use for external obligation - when someone else making a decision about what we must do
do have to	using MUST for questions is extremely formal. The verb we use usually in that case is...
didn't have to, didn't need to	the verbs we use for things that we did or didn't actually do
needn't have done	the only one verb we use for things that we actually did but weren't obliged to do