Hello! I am having some troubles understanding fibre bundles and I would be really grateful if someone can explain them to me in layman terms (at least how to visualize them). To begin with, I am not sure what is the fibre bundle, is it the projection function, or the total space (or something else)? I found an example of calculating the fibre bundles of ##S^1## with the fibre ##F= [-1,1]## and the results says that the fibre bundles are a cylinder or the Mobius strip. Based on this, I would say that the total space and the fibre bundle are the same thing, but then why 2 names for the same mathematical object? Also, as far as I understood, the fibre bundle is the union of the direct products of open covers of base space and the fibre, but this seem to straightforward for the definition fibre bundles have. So can someone explain to me how should I think of them? Thank you!