What is the topology of the structure group of a fiber bundle?

I dont know how can we topologize the structure group G of a fiber bundle P:E\rightarrow B by transition functions \psi_i^j (Osbern)

Do you know an easy and fundamental book on fiber and vector bundles? Thanks a lot

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Your question would be appropriate for the math.stackexchange website. Please look at the FAQ. In a fairly general situation $G$ is the group of homeomorphisms of the fibre with compact-open topology. Steenrod's "Fiber Bundles" book while a little dated is still a wonderful book. –  Ryan Budney Nov 3 '10 at 14:40