In the videos, the Geographic Information System that I use is ArcGIS, by ESRI. A free 180-day license of ArcGIS can be downloaded by clicking here. Conversely, if you wish, there are several good free GIS software packages that you can use. Two free GIS packages that are often used are GRASS and QGIS. ArcGIS is the industry standard, but both GRASS and QGIS are fine packages to use (and are open-source and free). I recommend using ArcGIS for this course and once you get the hang of it, move to GRASS or QGIS if you choose, the choice is, of course, yours.
The version of ArcGIS that you have may be different from the one used in the videos. In most cases, these are only small differences (like a button is in a different place) and can be resolved by a simple google search. If this is not the case, please e-mail email@example.com.