Kinda same question as this one on Volume 1 of Tu's manifold series Reference request: Best way of studying Loring Tu's "An Introduction to Manifolds" incompletely, but with restrictions, but I removed "Best way" because stackexchange told me my question might be subjective.
Now I ask for Volume 3, Connections, Curvature, and Characteristic Classes: What's the interdependence of the sections please?
Volume 3 contents except for last Chapter: Page 1, Page 2, Page 3, Page 4, Page 5, Page 6
For Volume 2 Differential Forms in Algebraic Topology (with Bott), Tu and Bott have a chart on a page called 'interdependence of the sections', whereas no such chart exists for Volumes 1 and 3 (Guess those volumes are not locally Euclidean since they don't have charts).
For Volume 1, I just started at Section 5 and discovered the interdependence as I went along. This answer on the above linked question seems to be consistent with my understanding of the interdependence.
For Volume 3, Tu gives a little hint in the preface.
In two decades of teaching from this manuscript, I have generally been able to cover the first twenty-five sections in one semester, assuming a one-semester course on manifolds as the prerequisite. By judiciously leaving some of the sections as independent reading material, for example, Sections 9, 15, and 26, I have been able to cover the first thirty sections in one semester.
Does this mean Sections 9, 15 and 26 are not prerequisites for the rest of the book? Anything else?
From Volume 1: "This book has been conceived as the first volume of a tetralogy on geometry and topology. The second volume is Differential Forms in Algebraic Topology cited above. I hope that Volume 3, Differential Geometry: Connections, Curvature, and Characteristic Classes, will soon see the light of day. Volume 4, Elements of Equivariant Cohomology, a long-running joint project with Raoul Bott before his passing away in 2005, is still under revision.