nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpq9g86fe4my0hhfks50t2049zlmstlfrwyd6kahh3fhg5xwc8lt3cqls5k3r (nprofile…5k3r) Have you encountered Frankel's "The Geometry of Physics"? It's purpose is develop those sorts of geometrical ideas and show their applicability to physics.
https://www.cambridge.org/core/books/geometry-of-physics/94894F70DB22055BD7BC2B84C135ABAF