What part of speech is “let”

'let' can be used as a verb, meaning 'to allow something to occur; to permit,' as in 'Please let me borrow your car.' In addition, 'let' can also be used as a synonym for 'rent,' as in 'I let out my apartment,' or 'We let a room in our house.' Finally, 'let' can be used as an auxiliary verb, helping other verbs to form tenses, moods, and voices. For example, 'let us go' (imperative mood of the verb 'go'), 'He had let them in' (Past Perfect), 'let it come' (Present Subjunctive), or 'Let them come' (Imperative mood of the verb 'come').

I let him go into the next room.

We let out the cottage for the summer holidays.

She let us use her computer.

the verb 'let' can also be used in an informal sense to introduce a suggestion or an offer 'Let's go for a walk,' 'Let me introduce you to my friend,' 'Let's take a break now,' etc.