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If $\pi: E \to M$ is a bundle over a topological space $M$, you can define a sheaf on $M$ that associates to each open set $U \subseteq M$ the set of sections over it, i.e., maps $\sigma: U \to E$ such that $\pi \circ \sigma = \mathrm{id}_{U}$. Conversely, given a sheaf $\mathcal{F}$ on $M$ you can construct a topological space such that your $\mathcal{F}$ is its sheaf of sections. This Wikipedia page has some information on it. You will also be able to find information on any introductory book an algebraic geometry (e.g., Hartshorne).