GIS concepts and tools are really useful and powerful for engaging geography and space in research and practice, but the learning curve can be steep.
Think about your learning style and use the tabs of this guide to find the resources that will best help you learn to do what you need to do with GIS.
A Gentle Introduction to GIS is an excellent free and open resource for learning GIS concepts.
In a similar vein, Essentials of Geographic Information Systems provides another overview of concepts regardless of which tool you're using.
GIS lets you map data and analyze it spatially.
GIS stands for Geographic Information Systems. GIS software allows you to view, understand, question, interpret, and visualize data in many ways that reveal relationships, patterns, and trends in the form of maps, globes, reports, and charts (definition from http://www.gis.com/ ).
The University of Michigan has a site license with ESRI for various ArcGIS titles, including ArcGIS for Desktop (including ArcMap), ArcGIS Pro, and ArcGIS Online. Information about installing desktop software is at http://www.itcs.umich.edu/sw-info/gis/arcgis.php
All or most Sites and CAEN computers and many other campus-unit administered machines have current versions of ArcGIS Desktop (includes ArcMap), ArcGIS Pro, and QGIS installed on them. These can also be accessed remotely through Virtual Sites.