Finally find a grammar book with enough exercises. For international students that's what I need.
It is written by British, but it includes comparisons of AE and BE in the appendix. Its advantages certainly overweight its disadvantages.
Since I have been learning English all these years, I did not read every page and do all the exercises. I use it in this way: quickly go over the notes and then decide whether I need exercises or the exercises is good enough for a try. It contains a lot of comparisons for learners like me, who always confuse two things. Some of the comparisons are even subtle than I expected.