When introducing tangent spaces on a manifold \({M^{n}}\), we defined the tangent bundle to be the set of tangent spaces at every point within the region of a coordinate chart \({U\rightarrow\mathbb{R}^{n}}\), i.e. it was defined as the cartesian product \({U\times\mathbb{R}^{n}}\). Globally, we had to use an atlas of charts covering \({M}\), with coordinate transformations \({\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}}\) defining how to consider a vector field across charts. We now want to take the same approach to define the global version of the tangent bundle, with analogs for frames and internal spaces.