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Everyone: Please forgive that I do not yet know LaTex, bro, and my English ( I am from UCV in Venezuela).

I think I understand concept of bundles almost well, and that, once a vector bundle with a fiber is known/given, that we can define a new fiber pointwise, in manipulating each of the fibers, e.g., we may change the fiber from being R (over itself) to being R(+)R, or from R to R(x)R ; RxR*, (dual)etc. What I not too clear on, is on how one put together all the new fibers coherently into a bundle, i.e., how one construct new trivializations and transition functions to turn the space with altered fiber into a new bundle. I am particularly interest in the quotient bundle, if someone knows. I imagine we use initial charts, trivialization to construct the altered bundle, but I don't see fully how, other than I pretty sure we use multilinear algebra and functoriality somehow. Would be great if someone knew about how to do this for general fiber bundles.

Thanks You from Caracas.

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