Mustn’t, Mayn’t, Mightn’t, and Oughtn’t
Mustn’t may be used in light conversation, but not in writing. The others should be avoided in speech and writing.
I’m, You’re, He’s, She’s, It’s, We’re, They’re
The contractions formed by compounding the pronoun with the verb are very common, and tend to preserve conversation from becoming stiff and formal. Nouns in the singular are sometimes compounded in like manner; as, “John’s going by the early train,” “Mary’s caught a bird.” Not many verbs beside is and has are thus compounded, and the practice should be discouraged.
Mayst, Mightst
Although mayst, canst, mightst, couldst, wouldst, and shouldst are contracted forms, the apostrophe is not employed to indicate the contraction.
Daren’t, Dursent
Dare not is sometimes contracted to daren’t and durst not to dursent, but the practice should not be encouraged.
Let’s
While verbs are often contracted when compounded with pronouns, as it’s, he’s, I’m, you’re, etc., the pronoun must not be contracted to form a combination with the verb. It may be a poor rule, but it will not work both ways. Let’s should therefore be let us.