Must expresses speaker's decision about necessity, while have to shows external obligation. Must is used in present tense only, have to for past and future. Questions are more common with have to, except in British English
Must expresses strong obligation and necessity. Must have + ed form indicates past deductions, not obligations. Must is used in spoken English to express reactions
Must and have to express mandatory obligations. Should indicates advice or opinion, not mandatory obligations. Must and should don't change for different subjects. Have to does change for different subjects
Can is used for both asking and giving permission. Could is more formal than can for asking permission. May is the most formal way to ask and give permission
Semi-modal verbs combine features of modal and main verbs. Unlike true modals, they can inflect for tense and person. They can take 'do' as auxiliary verb in negative and interrogative sentences
Oliver and Alfie visit pet shop where Amy works as veterinary assistant. Sophie discusses relationship with hamster Hannibal while flying in New Zealand