- let us (dated)
- Used to form the hortative of verbs, equivalent of the first-person plural imperative in some other languages.
- Let’s eat lunch sometime.
- Let’s dance.
Let’s is always inclusive, which refers to both the speaker and the addressee, while let us is commonly exclusive, which refers only to the speaker.
- Let’s go, we are late. - inclusive we
- Release us and let us go! - exclusive we
Negation of let's is let's not in standard English.
- Let’s not talk about it.
Don't is also used, but it is often considered non-standard.
- Let’s don’t talk about it. (US)
- Don’t let’s talk about it. (British)
Tag questions with let's typically take shall we?.
- Let's go to the beach, shall we?
- let, don’t let’s, let’s, let’s don’t, let’s not, The Columbia Guide to Standard American English, Kenneth G. Wilson, 1993.
- American English and British English, Concise Oxford Companion to the English Language, Tom McArthur, 1998.