We will follow the book "An Introduction to Manifolds" by Loring W. Tu. (Second Edition).
§1-6, 7.6, 7.7, §8, §9, 10.3, 11.1-11.4, 12.1, 12.2, §13, §14, §15, §16, §17, §18, §19, 20.4, §21, §22, §23, §24, §25, §26, §27 Appendices B.3, §C.
Through the university's web system, you can access this book here: https://link.springer.com/book/10.1007%2F978-1-4419-7400-6