I am studying Algebraic Topology written by Allen Hatcher. In page 58 the author gives some samples of infinitely many varieties of covering spaces of $S^1 \vee S^1$ i.e. figure-$8$-space. But I don't find any clear justification in this book as to why all of them are covering spaces of the figure-$8$-space. Also I am very eager to know the generators of such covering spaces mentioned in the same page. How do I justify them? Also how do I find the Galois group of those covering spaces on my own? What is the basic intuition behind that? I have tried to find out lecture notes from online source describing these facts explicitly but I have failed to find any of them. Can anybody help me by giving me some thoughts about that or by giving me some notes available online for free so that I can study them on my own and think independently?
Any help will be highly appreciated. Thank you very much.