Beginning Java from Wrox Press is a comprehensive look at the language by Ivor Horton. The first impression of the book is that it is big. Really big. If you decide that this isn't a book for you, then it could double up as a handy doorstop.
Ivor Horton has written many books on programming languages, and being an owner of one of these books (Beginning MFC), I know that he is good at explaining usually difficult concepts. Readers of these other books will not be disappointed, as Horton manages to explain each idea in an easy to understand way, yet in depth.
The first 10 chapters are dedicated to just getting to grips with the language and object orientation. The rest of the book describes how to design applets, how to use networks, and how to connect Java Applications to databases (JDBC).
Overall, the book provides a great introduction to Java. However, if you just want to learn Java to write applets, you may find this book is a bit long. It covers the applet issue by telling the reader how to convert an existing Java application into an applet. Basically, it may be too in depth for some readers. But if you wish to learn Java seriously, then this is the book to get.