Given finite CW complexes $X$ and $Y$ with $X$ connected, how can one go about computing the set of (baseless) homotopy classes of maps $[X, Y]$? Does a general procedure/algorithm exist?
I should say that I am primarily interested in the case where the space $X$ (and possibly also $Y$) has a low dimension, say $\mathrm{dim}(X)\leq 3$. Of course the problem is extremely hard in general.
I apologise if this is a stupid question, my background is in physics and I am not aware of any good references on this matter - if there are any then I would gratefully read them!