GIS (Geographic Information Systems)

QGIS is a free, robust, evolving, open source GIS application which began in 2002. It is supported by a large and devoted user community. 'Q' is platform agnostic and operates in Android, Linux, Mac OSX and Windows environments. The application has been translated into more than 40 languages and currently has over 1400 independently developed, functionality plugins which can be found at the QGIS Python Plugin Repository. 'Q' integrates easily with other open source GIS applications such as GRASS and PostGIS, and is considered to function on par with ArcGIS in terms of geoprocessing and spatial analysis capabilities.

QGIS Training Resources
QGIS documentation and training are provided and supported by a vibrant user community.  Follow the 'FOR USERS' and 'DOCUMENTATION' links for various guides, manuals, and tutorials.

Additional resources for Q

GeoDeltaLabs
A youtube channel with instructional videos covering ArcGIS, Google Earth, QGIS and other GIS related topics.

GRASS GIS (Geographic Resources Analysis Support System) is a free, open source GIS application inaugurated in 1982. It is platform agnostic and can operate in Linux, Mac OSX and Windows environments. Spatial analysis, image processing, raster data and statistics are its strengths. Links for the downloads, the documentation including manuals, tutorials, and sample data may be found here: GRASS GIS.

GeoDa is a free, open source GIS application specializing in spatial data statistics. Originally developed at the University of Illinois' Spatial Analysis Lab in 2003, it is now administered by the Center for Spatial Data Science at the University of Chicago.  It is a platform agnostic GIS and may be used in a Linux, Mac OSX and Windows environment.  Documentation, sample data, tutorials and the links for downloading the application may be found here: GeoDa

CARTO is a software as a service web platform which is an open source software built on PostGIS and PostgreSQL.  Its strengths include web mapping, spatial analysis and collected datasets.  There is a 12 month free version as well as a supported, subscription service.  Documentation and help can be found here: CARTO