This book is only readable AFTER you have read Schutz "Introduction to general relativity", the latter is a much better book.
One key flaw is that the author tries to cover lots of stuff in very little space, which requires read to take leap of faith. Lie group and Lie algebra are not covered well in this book.
"Tensor Analysis on Manifold" is a good alternative on differential geometry, but the fonts are too small.
