When I had about eight months of Java experience, I read the Core series. After reading Just Java 1.1, the core series were awful by comparison. They had a lot of errors coming from taking a book on 1.0 and sticking in a few 1.1 paragraphs and calling it a 1.1 book. I don't know if the 1.2 series is better - I haven't bothered to look since Just Java 1.2 works so well for me.(trailboss Jan 2000)
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.