Let him speak vs let him speaks

[Serzige]

Hi everyone!
I wonder why you don't have to put the S in the verb on this sort of sentence, "let her speak(s)". Well, for me, as a non-native English speaker, the "s" would have to go in there. I think all this is because of the third singular rule. However, I'm not sure about it, so I'd like you to explain it to me in more detail--if possible.

Thanks!
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Sergio M.
"Life is too short to grieve in sorrow"

[Mister Micawber]

Sergio, 'speak' here is an infinitive. The finite verb (that is, the one that inflects: speak, speaks. spoken, etc) is 'let':

I let her speak
He lets her speak
They have let her speak
I make them dance
She makes them dance
etc
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Native English teacher at Mister Micawber's

[Serzige]

Mister Micawber, thank you.
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Sergio M.
"Life is too short to grieve in sorrow"