Derived Geometric Regions
The Wolfram Language provides several ways of deriving new regions from existing ones, including combining them through Boolean operations and transforming them through a mapping.
Topological Operations
RegionBoundary — a region defined as the boundary of a region
Boolean Operations
RegionUnion — union of regions 
RegionIntersection — intersection of regions 
RegionDifference — difference of regions 
RegionSymmetricDifference — symmetric difference of regions 
BooleanRegion — any Boolean function of regions
Product Operations
RegionProduct — the Cartesian products of regions 
Sculpting Operations
ShellRegion — create a solid 3D shell by hollowing out the interior
Transformed Regions
RegionResize — resize a region while preserving the shape
TransformedRegion — a region as the image of a transformation
InverseTransformedRegion — a region as the inverse image of a transformation
Geometric Transformations »
RotationTransform — specify an arbitrary rotation
TranslationTransform ▪ ShearingTransform ▪ ReflectionTransform ▪ ...