[janm]

Transaction Processing: Concepts and Techniques (Jim Gray & Andreas Reuter) isn't just one of the best database textbooks, it is one of the best computer science textbooks. It is an Important Work.

On the other books, it depends on what you want. Alternatives to Date include Jeffrey Ullman, "Principles of Database and knowledge-base Systems" and "Foundations of Databases" by Abiteboul, Hull and Vianu.

As an introductory book, I like Database: Principles, Programming, Performance by Patrick O'Neil.

For more on transaction processing, as well as Jim Gray there is Philip Bernstein, eg "Principles of Transaction Processing".

Following the references is a lot of fun; see where you end up.