Not sure which books this review is supposed to cover since there are several "Core Java" books. However,
Core Java2 Volume 1 is an excellent book to get, particularly I think if you have previous programming experience. I'm not saying previous programming experience is required to use this book, but I did have a background with other languages when I picked this book up, and to me it made learning Java a snap. All the basics of the language are covered in here. This is the book I refer people in my office to who are just begininning work in Java.
Between this book, and
Core Servlets and JavaServer Pages, I learned all I needed to transition from other languages into being a productive web developer on the Java platform.