I am an junior currently taking a course on measure theory and Lebesgue integration using Royden's text. Before this, I took a standard intro to analysis course covering the first seven chapters of baby Rudin. My institution doesn't offer a multivariable analysis course. I have room in my schedule next semester for two independent studies on topics of my choice. I want to go to graduate school to pursue a PhD in math and do not want to have any holes in my undergraduate preparation. I'm not yet sure what I direction I want to go in during grad school.
Would it be worthwhile for someone in my situation to do an independent study using a book such as Munkres' Analysis on Manifolds or similar such as Spivak's?