Modal verbs in English grammar express the ability, permission, obligation, possibility, etc. Modal verbs only have one form, meaning that they are used in simple present and don't have past simple and past participle forms.
However, some modal verbs can have alternative forms which can be used in different tenses.
She can dance.
Can is a modal verb that expresses the ability to dance in the simple present tense.
She could dance.
Could is an alternative form of can, which can be used in the past simple tense.
Rule 1: We use can to express ability only in the simple present tense.
My mother can understand the meaning of French songs.
Can expresses the ability to understand in simple present.
Rule 2: We can use an alternative form to be able to to express ability in all tenses (present, past, perfect, continuous, and future).
My mother will be able to understand the meaning of French songs once she finishes her language course.
Will be able to is an alternative form of can that expresses the ability to understand in the future tense.
Rule 3: We can use an alternative form could to express the general ability and with the verbs feel, hear, see, smell, taste, remember and understand in past simple.
My mother could understand the meaning of French songs when she was studying French.
Could is an alternative form of can used to express the ability to understand in past simple.
Rule 4: We can use an alternative form was/were able to to talk about something specific in the past simple.
Was your mother able to understand that popular Mylene Farmer's song?
Was able to is an alternative form of can used to talk about a specific ability in the past.
Rule 5: We can use both can and could to ask permission in present simple. Could is more polite than can.
Can/Could I leave my bag here while I wait?
Both can and could are used to ask for permission.
Rule 6: We can only use can to give permission.
You can leave your bag here.
Can is used to give permission to leave the bag.
Rule 7: We use could in conditional clauses and in the simple past.
She could leave her bag here if she wanted to.
Could is used in the second conditional.
Rule 8: We use can't (a short form of cannot) to express something we are sure is untrue or impossible in the present.
He can't be retired, he's 15 years old.
Can't is used to express an impossible event in the present.
Rule 9: We use can’t + have + past participle to speculate about something in the past.
He can't have worked very hard.
Can't have worked is used to speculate about his hard work in the past.
Rule 10: We use both couldn’t (could + not) and wasn’t/weren’t able to (was + not/were + not able to) to create negative forms.
My father couldn't/wasn't able to learn a foreign language.
Both couldn't and wasn't able to express a father's inability to learn a foreign language.
Choose the correct modal verb: I ___ come to your party tonight.