I've been self studying differential geometry for a little while now (4-6 months). I am learning from Lee's *Introduction to Smooth Manifolds*, and I just don't quite get the point of the subject. Why do we study the constructions that we study, such as differential forms, submanifolds, vector bundles, etc. ? What is the goal of differential geometry, i.e., what is the motivation for studying it?

Edit: As Will Sawin suggested, I will describe things I find motivating. I find beautiful structures, unsolved problems, and a general goal of what we are trying to do in the subject to be motivating. For instance, the motivation in topology (point-set) is to find topological invariants of a given space. This leads us to connectedness, compactness, the fundamental group, etc. In this example, we have a general rule for what we are trying to accomplish. What is this such rule in differential geometry?