Infinitives and Base

[Aikuzo]

Infinitive
I want to work
He has to sing.
This exercise is easy to do.
Let him have one.
To be, or not to be, that is the question:

Base - Imperative
Work well!
Make this.
Have a nice day.
Be quiet!
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I'm a complete newbie here sob. Could someone explain what are infinitive and base. I mean what makes a sentence infinitive and what makes it a base. Do you have additional resources that tells me more about this?

Thanks in advance.
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I quit studying English years ago and have just come back to study the basics.