In this mini-course, we are going to cover Chapter 5 of Spivak’s Calculus on Manifolds book. We started this Chapter in Math 174, but we did not finish it. I will review the part of the chapter that we already covered in the course for the sake of those participants who did not take the course. This mini-course is going to run on Wednesdays for several weeks. Today it will run for an hours, but the subsequent lectures will be longer.