The Definitive Guide to SQLite is a great new book from Apress. While it covers SQLite deeply (easily living up to its title), it also provides a resonable introduction to RDBMs and SQL.
It has a solid chapter (nearly 50 pages) on the Core C API (for using SQLite), and another (also nearly 50 pages) on the Extension C API (for extending SQLite). While I'm partial to Ruby, and found the coverage of the Ruby SQLite library to be quite good, other languages seem to get solid coverage as well.
The book isn't just aimed at users though. There's a chapter on the architecture of SQLite and another on its internals, if you've got a hankering to start developing.
SQLite seems like a lightweight database on the rise. Its portability, small size, speed, and liberal licensing (it's in the public domain) make SQLlite an attractive choice for a number of systems. Maybe your next application is one of them.
If you're using SQLite now, or think you might be soon, you owe it to yourself to buy a copy of this book.