Public SQL database for educational purposes

If SQL Server is an option then Northwind/Adventureworks are the standard "training" DBs. Do a search.

For mySql this project looks promising:

http://sourceforge.net/projects/awmysql/

Also, this might be a dupe:

Is there a "Northwind" type database available for MySQL?

Where can I download Northwind database for Postgresql?

I would suggest setting up Microsoft SQL Server 2008 Express (or the R2), and adding the Northwind or Adventureworks database. It's pretty big so I'm sure you can play with it.

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