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.
Please guide me which is the best book for core java??
Well, there's no the best book for Core Java. However, there are many excellent books to learn Core Java.
Can you give us a little background? Is it your first book to Java? First book to Object Oriented programming? First book to computer programming in general?
If you don't know anything about OO concepts, then you can either choose a good OOM&D (Object Oriented Modelling & Design) book like Design Patterns by GoF(Gang of Four), Head First OO etc.
If you are aware about OO concepts, then nothing beats Core Java(volume I & II) by Horstmann & Cornell. But make sure that you've properly understood OO concepts, because this book, as its name says, is specific to Core Java and not about OO concepts in general.
If you want to learn only those OOM&D concepts which are required to learn Core Java, and then continue learning Core Java, then you can check out Head First Java, Thinking in Java, Java How to Program, Java Complete Reference etc.