Your own recommendations

Designing Databases

Database Design for Mere Mortals
by Michael J. Hernandez
Very basic-level stuff, well-handled. Useful if you are a complete newcomer to RDBMS.
Data Modeling Essentials

Data Modeling Essentials: Analysis, Design and Innovation
by Graeme Simsion
THE book for learning from the ground up about data analysis, relationships, normalization and creative ways to solve tough problems. Read this book before you read any other - everything else is just a follow-up.
Mere Mortals

Database Design for Smarties
by Robert J. Muller
Very sound UML approach to designing databases. Not specific to relational databases.
Joe Celko's...
Joe Celko's Instant SQL Programming

Instant SQL Programming
Probably not one of Celko's finest works. Not a beginner book, either
Joe Celko's Data and Databases

SQL For Smarties: Advanced SQL Programming
New edition of the classic book of magic spells for SQL programming.

SQL Puzzles and Answers
Hands-on approach to beating your SQL task into shape.
Joe Celko's Data and Databases
Data and Databases: Concepts in Practice
Not exactly a primer, but this book contains a good deal of material to cure you of the "spreadsheet mentality" when designing and mending databases.
SQL Reference

The Practical SQL Handbook
by Judith S. Bowman et al.
How-to and desktop reference for standard SQL, well-reviewed.

SQL: The Complete Reference
by James Groff and Paul Heinberg
Guide to SQL Standard

A guide to the SQL Standard
by Hugh Darwen and Chris Date
Essence of SQL

The Essence of SQL
by David Rozenshtein and Tom Bondur
Very concise, very much a beginner book.
SQL Fundamentals

SQL Fundamentals
by John Patrick
Oracle and Access focused.
Clearly Explained

SQL Clearly Explained
by Jan Harrington
Beginner-to-intermediate level, thin on discussion of relational concepts but otherwise considered a good starter book. Same author has written Relational Database Design Clearly Explained.
Understanding the New SQL

Understanding the New SQL: a Complete Guide
by Jim Melton and Alan Simon
Covers SQL-89 and SQL-92, comprehensive, good lookup reference.
Understanding SQL

Understanding SQL
by Martin Gruber
It's been around a while but it still gets rave reviews from folk who have had to learn SQL the hard way in the past.

SQL for Dummies
by Allen G. Taylor
As expected, no great depths are sounded here but it uses Borland C++ and Delphi for client examples. Good if you don't want to face the big challenges for a while.
Teach Yourself
Teach Yourself in 24 Hours

Teach Yourself SQL in 24 Hours
by Ronald Plew
Weekend pressure-cooker. Gets approval for being a straightforward introduction.
Teach Yourself in 10 Minutes

Teach Yourself SQL in 10 Minutes
by Ben Forta
Speed-reading skills essential . Good reviews for being direct and a quick way to get to grips with queries.
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