Date: 2023-10-26 | Article ID: 70621 |

The concept of a **gauge field** in classical physics is based on the mathematical concept of a **principal bundle**. Some other classical fields that interact with gauge fields are based on the concept of **vector bundles** that are **associated** with the principal bundle. This article introduces principal bundles and vector bundles as specializations of the general concept of a **fiber bundle**. This is a prerequisite for article 76708, which explains how these things relate to the concept of a gauge field.

**2023-10-26**(deleted a stray subscript, deleted a stray parenthesis, added some vocabulary)**2023-10-05**(corrected a statement in a caption about the significance of the dashed lines, fixed a notation discrepancy in a figure, added a footnote about line bundles, added a reference)**2023-10-01**(first version)

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