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Have now worked through 9 chapters of the course book and am about halfway through TMA03.  Finally getting to the good stuff - surfaces, curvature, Riemann tensor, parallel transport; all the machinery for general relativity.

I'm still finding the textbook hard.  It makes massive jumps, and hides many of the important results in the exercises.  I've never worked through any maths as slowly as this.  The other thing that is lacking is worked examples.  There are solutions in the course notes to many of the exercises, but again these are pretty brief.  Calculations in differential geometry always seem to involve masses of tedious algebra with multiple subscripts, superscripts and exponents, which confuses things horribly.

I'm definitely getting there though.  Will be back to number theory again soon, but will be looking forward to chapter 10 - manifolds!