I got some interest in String Theory when I was listening to lectures of David Tong and Brian Greene. I remember them stating that the spacetime manifold is compactified to resemble our usual 3+1 dimensions, using Calabi Yau Manifolds. But String Theory offers a lot of different possibilities of Calabi - Yau Manifolds one of which may resemble our universe.

And the other point is, if we let the strings(particles) vibrate in a particular manifold, we can essentially compute the physical constant related to it.

So, my question is, can I have resources like reviews, textbooks and any other resources related to this which will help me compute the physical constants from a given Calabi-Yau Manifold?

My Background: I know QFT in the level of Peskin. I know General Topology and Differential Geometry to some extent(I have taken a course in General Relativity, equivalent to Eric Poisson's lectures here)

Addendum: I don't know how to compute constants from a manifold, I also don't know how those manifolds are represented(metric or connections??). I also don't know how much math is required as a prerequisite. I would be glad if you can share me with a roadmap to reach the above state.