I am no longer lecturing this course, and the syllabus has changed.
Please check the official course websites for relevant information. I have left this archive available for anyone interested.
Notes for course of 2012.
Handwritten solutions by Tom Collyer:
Geometry of Surfaces course notes
by Nigel Hitchin at the University of Oxford
(particularly Chapter 4, a.k.a. "Chapter 3, Surfaces in R^3"!) give a very nice concise introduction.
I used some material from this in preparing the course.
This course has a MathsStuff page, where you can find some ``archived material'' from long ago.
Animation (Mathematics Museum, Ibaraki University.)
Interactive (Visual geometry, Technische Universitat, Berlin.)
Stills (Minimal surfaces, Indiana University.)
(1) John McCleary, "Geometry from a differential viewpont" :
Cambridge University Press 1994. (QA 641 M2).
[A more modern account of some classical material. Some material was used in preparing this course.]
(2) Dirk J. Struik, "Lectures on classical differential geometry" :
Addison-Wesley 1950 (QA 641 S8).
[Classical treatment, good reference for much of the material].
(3) Manfredo P. do Carmo, "Differential geometry of curves and surfaces" :
Prentice-Hall 1976 (QA 641 C2).
[More traditional approach. Lots of examples.]
(4) Barrett O'Neill, "Elementary differential geometry" :
Academic Press 1 1966 (QA 641 O6).
[More general introduction to classical differential geometry, with sections on curves and surfaces.]
(5) Sebastian Montiel, Antonio Ros, "Curves and surfaces",
American Mathematical Society 1998 (QA 643 M6613).
[More modern and advanced treatment.]
(6) Alfred Gray, "Modern differential geometry of curves and surfaces" :
CRC Press 1993 (QA 641 G7).
[Practical introduction to curves and surfaces, with many illustrations.]