In this thread I am going to build a principle bundle based on the torus. The advantage of this ultra simple case is that everything can be visualized. The disadvantage is that some things are really too simple to convey what needs to be conveyed. When I hit one of those points I will add some extra comment in bold face to try to cover the problem. There is one other thing. I am going to start a second thread on this boqard to hold your comments. Please be kind to those reading about the model by putting all comments and criticisms of my development on that thread rather than this one. It makes it hard to read when there are many posts inline. If your ideas turn out better than mine I can always edit the posts on this thread. Before I introduce the toy model in the next post, let me say a bit about principle bundles. We have had some discussions recently about connections and metrics on manifolds. Principle bundles give a way to introduce connections on manifolds without using metrics. The thing that does it is the connection 1-form and we will see how this arises. Principle bundles are an example of a more general structure called a fiber bundle. General fiber bundle theory is a large topic and an important part of differntial geometry. Principle bundles, as the name might imply, are central to that theory because they can be used to construct other bundles. We won't go into that aspect of them here. I will be introducing the various "parts" of a fiber bundle as well as a principle bundle in the next post on this thread.