let us
let's
let usYou use let's when you are suggesting that you and someone else should do something. Let's is short for 'let us'. It is followed by an infinitive without to.
The full form let us is used with this meaning only in formal English.
If you are suggesting that you and someone else should not do something, you say let's not.
When you are talking about you and someone else being allowed to do something, use let us.
You can use let us when you are making a request on behalf of yourself and someone else. In sentences like these, don't shorten let us to 'let's'.