Light weighed: on the statistics and systematics of weak gravitational lensing

In astronomy, the interpration of observations and measurements plays a crucial role: we rely purely and fundamentally on the information that reaches us as observers. And 80% of all matter in the universe is undetectable directly.This so called 'dark matter' can be observed indirectly, by the gravitational effect on its surroundings and the curvature of spacetime predicted by the theory of relativity.In this thesis, we combine scientific research, a description of our universe, with theoretical considerations of the statistical methods used for that research, or how we can deduce that description from the 'reflections' that we see. In this work, we focus on the matter distribution in groups and clusters of galaxies, and consider the intricacies of the method of weak gravitational lensing that we use, respectively. Galaxie