Would be taking up a course on spatial databases next semester.
Would anybody know a newbie friendly introductory resource?
A vendor neutral one would be preferable.
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I strongly recommend the book "PostGIS in Action" by Regina Obe and Leo Hsu.
They are the same people who run the Boston GIS site mentioned above.
The book goes into a lot of detail about PostGIS but the concepts transfer well to other platforms.
Beginning Spatial with SQL Server 2008 would definitely be helpful even though it is specific to SQL Server. For now at least, SQL Server seems to be one of the better platforms for leaning about spatial SQL operations.
SQL Server Express is free and will give you full access to the same spatial capabilities you would get with the Enterprise version.
For Spatialite, the best resource is the official doc. The main developers are maintaining a great cookbook and it's oriented general spatial database too. It's really good material for beginners.
See also OSGeo's Searchable Database of Educational Material for courseware: http://www.osgeo.org/educational_content