How and where to learn maths theory for economics?

Hi everybody

I am currently studying Applied Economics. This means that I have gotten math and econometrics classes, but without the mathematical theory part (so just exercises etc).
Now, I would like to switch to a proper (pure) Economics degree. This means that I will have to catch up on mathematical theory, learn to write proofs, learn to read maths theory, …

BUT, I can not (properly) do this yet. I have until next year's september to learn the basics.
I believe that this is possible, as I am a very disciplined individual but I lack guidance.

I need book recommendations and help with topics which I should and should not do, as I progress through the levels of math.

I would love a book solely focused on mathematical theory and a book focused on proof writing as I have never done this.

Thanks in advance!