Random tessellations: Stereological formulae in Euclidean space and Kendall's Problem in spherical space

In the first part of this thesis, a stationary tessellation in Euclidean space and its intersection with a linear subspace are considered. The main result of this part is a relation between the Palm measures of a random measure living on the original tessellation and a random measure living on the intersection. In the second part, tessellations in spherical space are investigated. A spherical analogue of what became known as 'Kendall's Problem' is formulated and investigated.