You can find here
a set of notes for the Part IID course Differential Geometry.
Thanks for all the corrections and comments that I received when I lectured the course. Special thanks go to Owen Jones. More recently, Pelham Wilson provided me with many insightful corrections.
There is nothing in these notes that cannot be found in the various excellent texts which I followed.
You are very much urged to look at them. My favourites are:
* DoCarmo, Differential Geometry of Curves and Surfaces;
* Guillemin & Pollack, Differential Topology;
* Milnor, Topology from the Differentiable Viewpoint;
* Spivak's volumes II and III of his Comprehensive Introduction to Differential Geometry.
Spivak's volumes are superb; pay particular attention to his remarks on Gauss' paper.
I very much welcome comments and/or corrections on the notes.
Last updated: 28/11/12
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