Database Management Systems by Raghu Ramakrishnan and Johannes Gehrke
An Introduction to Data Base Systems by C.J. Date
The "red book": Readings in Database Systems, which is a collection of basic papers from the field. This is used by DB programs in top schools (eg. Berkeley).
The "Jim Gray book": Transaction Processing. Look up Jim Gray to see why this may be worth looking into.
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.
I learned from this book. I also know a few graduate students who studied databases (or some varient) and they continued to use this book throughout their studies.
(I know nothing of the other book though, so this is a one-sided view)