I was reading chapter $12$ of John Lee's Book on Topological Manifolds.
Let $X$ be a topological space that has a universal covering space, and let $x_0\in X$ be any base point. There is a one to one correspondence between isomorphism classes of coverings of $X$ and conjugacy classes of subgroups of $\pi_{1}(X,x_0)$. The correspondence associates each covering $\hat{q}:\hat{E} \rightarrow X$ with the conjugacy class of its induced subgroup.
So using this theorem we can classify the torus coverings. There are exactly three.
My question is the following: do we have similar kind of classification theorem for coverings of $P^1$, If yes kindly mention the reference. If the problem is still not solved, what is the progress made.
First of all, $\pi_1(\text{torus}) = \mathbb Z\oplus \mathbb Z$ and there are infinitely many subgroups. So the number of isomorphic class of torus covering is not three.
On the other hand, $\mathbb P^1$ is simply connected (I assume you are talking about the complex projective space) so there is only one covering up to isomorphism, the trivial one.