Stochastic geometry, based on current developments in geometry,
probability and measure theory, makes possible modeling of two- and
three-dimensional random objects with interactions as they appear
in the microstructure of materials, biological tissues,
macroscopically in soil, geological sediments etc. In combination
with spatial statistics it is used for the solution of practical
problems such as the description of spatial arrangements and the
estimation of object characteristics. A related field is
stereology, which makes possible inference on the structures, based
on lower-dimensional observations. Unfolding problems for particle
systems and extremes of particle characteristics are studied. The
reader can learn about current developments in stochastic geometry
with mathematical rigor on one hand and find applications to real
microstructure analysis in natural and material sciences on the
other hand.
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