The book, as the title suggests, is a good introduction to global economic history. I read this for a class about the subject and I felt the book provided me with quite a good base knowledge on the subject. Now I do personally find economics history quite boring, but I cannot fault the book for that. Overall a good, short book about the subject.
The only real critique I can come up with is that Allen tends to be a bit eurocentric in the facts he provides and topics he discusses in the book. Allen also tends to be a bit one-sided when studying events such as the industrial revolution, mainly focusing on all its positives. But I can understand why the author would keep it simple for a book like this.