Verb conjugation and contraction - in other words; "The short form".
In spoken English we use the short form a lot. We say things like: I'm / you're / didn't etc. instead of I am / you are / did not etc.
We also use these short forms in informal written English. When we write in the short form, we use an apostrophe (') for the missing letter(s).
Forms of the auxiliary verbs to be, to do and to have:
To be - Simple Present Form
To be - Simple Past Form
To do - Simple Present Form
To do - Simple Past Form
To have - Simple Present Form
To have - Simple Past Form
The long and short forms of the modal verbs can, could, shall, should, must, will and would
Can
Let us is a funny one. The only time I've ever heard the long form of "Let us..." used is when the vicar used to say "Let us pray." It's much more likely you'll hear or see the contracted form "let's". "Let's do this," no "Let's do that instead," and the sarcastic "Oh yes, let's."