A Most Incomprehensible Thing by Peter Collier - highly recommended to the educated layman with a strong interest in modern mathematical physics and to teacher training students. Not a general textbook-style overview for physics students studying for their exams, but a good start.
This is a book about one of the most fascinating fields of science - General Relativity. If you REALLY want to know about black holes and cosmology, but know just high school mathematics to start with - this is your book. It's intended for self-study, which means you have to sit down with it and work your way through some math which is quite far above high school level. BUT: If you're looking for a quick overview, and hate equations, then this is not your cup of tea.
You're still reading - you do want to know about Schwarzschild's solutions to the Einstein Field Equations! "Notes toward a (very) gentle introduction to the mathematics of relativity", that is what this book really is. Most importantly, here's an author who doesn't show off how good he is, and how easy this most complex topic is to him - every experienced reader knows that most authors do just that. While having carefully read two thirds of the book as of now, I never even once found the phrase "it is simple to calculate this...", or, "as the reader can easily see...", or something else that makes me angry about many scientific textbooks. Do you know the feeling?
One day, you may want to read Misner, Thorne and Wheeler's "Gravitation". If you're not a physics graduate, you might want to start with Schutz's "First Course in General Relativity" - my next book, already waiting. Collier's book might be your stepping stone toward that - that's my approach, anyway. Can tell you in a couple of years if it worked.
Now about the contents:
General Relativity, that is something you shouldn't try to tackle without some background. So, Mr Collier starts with basic mathematics, and works his way up to calculus, vector geometry and all the other stuff you need. Just hop on at the place where your math runs out, and follow his lead. It may not be the best book on trigonometry and functions and such stuff, but it's alright. It's strong side is about the parts which high school doesn't teach.
Then comes the first really interesting part: Special Relativity. From the basic axioms (the speed of light is always the same, whatever the observer's speed, and so on) up to the consequences (time runs slower if you're in in a very fast spaceship,...), everything is shown using the real scientific methods (metric tensors, Lorentz transformations, Minkowski diagrams, invariant hyperbolas), but slowly and with every essential calculation completely written down. You will find out all you need about flat spacetime and finally why energy and mass are connected by the most famous of equations, E = mc². Everything is also presented visually, as far as possible.
As you take one step after the other, it's vectors, matrices, tensors you have to get to know. Of course, there will be lots of partial derivates, but you need them. Then, you will approach curved spacetime, which is what GR is all about. Well, this is where I stand, after about six weeks.
This review will be completed once I've finished the book. I've enjoyed every chapter of it so far and can hardly wait reading about GR's applications. If you're like that, give the book a try. It doesn't cover all of GR, though - no gravitational waves, for instance. But Mercury's perihelion shift, gravitational lenses, time dilation and redshift, black holes and cosmology are all covered.
Your journey has just begun!