may May I have another cup of coffee? = used for asking for permission China may become a major economic power.= Future possibility ...................................... shall Shall I help you with your luggage? = offer Shall we say 2.30 then? = Suggestion Shall I do that or will you? = Asking what to do

"Can" is what you are able to do, or is a suggestion, "may" is what you are allowed to do. "Shall" is what you will do, and "should" is both subjunctive, meaning what you ought to do but may not necessarily do, as in a suggestion, or an obligation in the second meaning. It all depends on context.

May 1. polite request - affirmative questions Мay I use your telephone, please? - Не разрешите ли воспользоваться вашим телефоном? May I open the window, please? - Можно ли мне открыть окно? 2. formal permission - affirmative and negative statements and affirmative questions You may stay here only for 4 days. - Вам разрешено остаться здесь только на 4 дня. May I come in? - Можно мне войти? Yes, you may. - Да, можно. No, you may not. - Нет, нельзя. 3. possibility - affirmative and negative statements I'm not sure, but he may be at school now. - Я не уверен, но он возможно в школе сейчас. He may not be home yet. - Возможно, что его еще нет дома. He may have seen Marina yesterday. - Он, возможно, виделся с Мариной вчера. Shall -- suggestion of some activity - affirmative questions Shall I read? - Мне читать? Shall we dance? - Потанцуем? Shall we? - Начнем? Should 1. advice - affirmative and negative statements and questions You look ill, you should see a doctor. - Вы выглядите больным, вам следует пойти к врачу. Should I ask Alexandrе about it? - Следует ли мне спросить Александра об этом? 2. strong probability - affirmative and negative statements, future and past This book should be interesting. - Эта книга должна быть интересной.) This task shouldn't be difficult for you. - Это задание не должно быть трудным для вас.

should We should sort out this problem at once. = Saying what’s right or correct I think we should check everything again.= Recommending action Profits should increase next year. = Uncertain prediction

Can They can control their own budgets. = used to show Ability / Possibility We can’t fix it. = used to show Inability / Impossibility Can I smoke here? = used for asking permission Can you help me? = used to request