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Projection and reprojection can be done using ArcGIS (yes, obviously) but also using the open source library proj4. Luckily, many projects linked to proj4, such as R (package rgdal, function spTransform) and PostGIS

INSPIRE I have two fat reports by INSPIRE in my office, one defines the INSPIRE grid (and its projection), the other is on projections for Europe. I will try to digest them and report some essential information here, including examples of geographical reprojection with R.