In my opinion this book and "A First Course in General Relativity by Bernard F. Schutz" are perfect complementary texts to learn the main basis of General Relativity on your own.

The author has provided an unbelievable amount of questions and not a single one of them is pointless exercise.

The book is Divided into three sections:

Part 1: Metric description of Space-Time
Very well written intro to General Relativity which delves into Black Holes and Mercury's Orbit, without the full on Field Equation and Tensors.

Part 2: Cosmology
Still keeping to the metric description of space-time, cosmology is introduced. The mathematics of concepts like the closed and open universes are explained really well.

Part 3: Full Tensor Formulism
I was able to learn Tensors from this, using Chapter 3 from Schutz's book as a companion.

The questions at the end of each chapter really test your knowledge and after reading this you will be able to manipulate the field equation for simple cases and move onto more advanced books if you wish.