I am no longer lecturing this course and the syllabus has changed.
Please check the official course websites for relevant information.
The course also has an Offical web page.
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Prior to 2014, a course with the same title was given as a 4th-year module. The course notes above give a nice account of much of the material in the current 3rd year unit. Lots of pictures, more examples and explanations. I have used it in preparing my own notes. It covers most (but not all) of the current course, and lots more. (There is a lot of stuff about transversality which is not in the present course. Conversely, I was planning to say something about general vector bundles, which is not discussed in these notes.)
Sphere eversions: turning a sphere inside out through immersions: Scary video: Optiverse video and explanations: Optiverse page
Mechanical linkages: manifolds as configuration spaces: WP page, and a paper by (our very own) Magalhaes and Pollicott here, with reference to the Thurston-Weeks Linkage (surface of genus 2).
L. W. Tu, ``An Introduction to Manifolds'', Universitext Springer-Verlag (2010).
QA613.T8.
[Covers most of the material in the course fairly efficiently.]
J. M. Lee, ``Introduction to Smooth Manifolds'', Graduate Texts in
Mathematics, Springer (2013).
QA613.L3.
[Good introductory text. Develops the theory from basic material to
more advanced topics. Covers most of the course. 600+ pages.]
F. Warner,
``Foundations of differentiable manifolds and Lie groups'', Graduate Texts in
Mathematics, Springer (2010).
QA614.3.W2.
[A more formal treatment. Progresses quite quite quicky on to
more advanced topics.]
W. Boothby, ``An introduction to differentiable manifolds and Riemannian geometry'', Academic Press (2003). QA614.3.B6.