Tutorials and introductions to GIS can be found on the web. GIS.com (another site from ESRI) offers a very nice introduction, including explanations of GIS, geographical and cartographical concepts, and links to live data, data for download, and more information.

Also, try a general web search for gis tutorials and limit to educational instututions. For example, in Google, type:

"gis tutorial" site:.edu

The GIS community is an active one and there are many listservs and blogs to which you can subscribe, for example, Free GIS Data & Imagery GeoBlog.