Listen to the difference between these two sentences. I swim. I can swim. That one small word changes the meaning completely, because now we're talking about ability.
Modal verbs are helping verbs. We use them with another verb to add meaning like ability, obligation, possibility, or advice. The main modals are can, could, may, might, must, shall, should, will and would. You'll also hear semi-modals like have to, ought to and need to.
The first rule is simple. After a modal, use the base form of the verb. We say can swim, not can to swim. The second rule stays fixed in every subject: he can swim is correct, and we never add an s and say he cans swim. The third rule changes questions and negatives — with modals we don't use do, so we say Can you swim and You can't swim.
So the pattern stays neat. Modal, then base verb, and no do-support. That's why modals feel different from most other verbs in English.
We usually use can for ability in the present. You can join a summer course at Loxdale if you want to improve your English quickly. Could often talks about past general ability: when I was younger, I could swim for hours. It can also make a request sound more polite, like Could you help me, please.
For one specific past success, could is often not the best choice. If you finally found the right classroom on your first day, you'd usually say I was able to find it, or I managed to find it. Could is fine for general past ability, but one successful moment often needs was able to or managed to.
Now let's move to obligation. Must and have to can both show that something is necessary, but the feeling is slightly different. Must often sounds more like the speaker's rule or strong feeling. Have to often sounds more practical, like a system or a timetable. At Loxdale, students have to register on the first Monday, so have to fits naturally there.
The big contrast is this. Mustn't means it is prohibited. Don't have to means it is not necessary. You mustn't miss registration if the school requires it, but you don't have to bring every book on the first day if the school provides materials.
We often use may, might and could when something is possible but not certain. It might rain this afternoon means maybe yes, maybe no. Could can also express possibility, especially when you're considering one option among others: we could go to Brighton after class if the weather stays good. May can sound a little more formal, and it's also used for permission — you may leave the classroom now.
For advice, should is usually the most common choice. You should check your timetable before classes start. Ought to is close in meaning but a little less common in everyday speech. Had better is stronger and often carries a warning: you'd better register on the first Monday, or you could miss important information. Should can also express expectation — the teacher should be here by nine.
When we talk about past possibilities or past judgements, we often use a modal, then have, then the past participle. For certainty, must have: she must have missed the bus. For criticism, should have: you should have emailed earlier. For impossibility, can't have: he can't have understood the message. For possibility, may have, might have or could have.
In fast spoken English these forms often contract — should've, could've, might've. If you can recognise those sounds, real conversation becomes much easier to follow.
So: modals for ability, obligation, possibility, advice and past meaning, plus the core rules. No to after the modal, no third-person s, and no do-support. Now try this. You forgot to register on Monday. What should you say? The best answer is I should have registered earlier — or in natural speech, I should've registered earlier.