This week's book giveaway is in the OO, Patterns, UML and Refactoring forum. We're giving away four copies of Refactoring for Software Design Smells: Managing Technical Debt and have Girish Suryanarayana, Ganesh Samarthyam & Tushar Sharma on-line! See this thread for details.
"Core Java" is the name of a couple of well-known books about Java; "core" in this context means the central, most important part (although the books don't really have such a focus.) Otherwise, there's no formal, specific thing called "core Java".