Trainings selected via http://training.esri.com/gateway/index.cfm?fa=search.results&cannedsearch=2 assume ArcMap version 10.x, noted * 9.3 if applicable. If you see another free training you would like to do instead, please identify it - otherwise, start here.
Authoring Web Maps Using ArcGIS Online http://training.esri.com/gateway/index.cfm?fa=catalog.webCourseDetail&courseid=2519
Creating a Common Operational Picture with ArcGIS (9.3) http://training.esri.com/gateway/index.cfm?fa=catalog.webCourseDetail&courseid=1743
Creating Map Books Using Data Driven Pages http://training.esri.com/gateway/index.cfm?fa=catalog.webCourseDetail&courseid=2152
Using Network Analyst in ArcGIS Desktop 10 http://training.esri.com/gateway/index.cfm?fa=catalog.webCourseDetail&courseid=1955
Python for Everyone Using ArcGIS 10.1 http://training.esri.com/gateway/index.cfm?fa=catalog.webCourseDetail&courseid=2520
Using Python in ArcGIS Desktop 10 http://training.esri.com/gateway/index.cfm?fa=catalog.webCourseDetail&courseid=1868