Handbook of Effective Writing by Robert Hamilton Moore covers grammar, syntax, and writing. It has been my English-language primer since high school. The 1965 edition begins with a chapter that addresses some of the most common errors in grammer: fragments, run-on sentences, subject + verb agreement, and comma splices.
What the book really nails is the problem of awkwardness. It’s a complex problem which may take many forms and may be related at one and the same time to weakness in grammar, to shifts in construction, to the uncertainly in diction and idiom which plagues those who have never done much reading.
Shortly after I came to America, when I was in 7th grade, my writing had a lot of room for improvement. Awkwardness was the biggest problem. It was very hard even for my teacher to finger a finger on, because awkwardness results in writing which is not exactly ungrammatical but is certainly not fluent. This book, along with practice in writing, reading (a lot of reading, as you can tell), and reading aloud what I have written really helps me in English skills.