Geometric measure theory studies geometric properties of non-smooth
sets. The key concept is that of an n-rectifiable set, which can be
parametrised by countably many Lipschitz images of n-dimensional
Euclidean space. Characterisations of rectifiable subsets of Euclidean
space have important consequences in the theory of partial differential
equations, harmonic analysis and fractal geometry.

The recent interest in analysis in non-Euclidean metric spaces naturally
leads to questions regarding geometric measure theory in this setting.
This talk will give an overview of work in this direction. After
introducing the necessary background, we will present recent
characterisations of rectifiable subsets of an arbitrary metric space in
terms of tangent spaces.