Gravitational Lensing
Matthias Bartelmann (Zentrum fuer Astronomie der Universitaet, Heidelberg, Institut fuer Theoretische Astrophysik)

TL;DR
Gravitational lensing is a crucial observational tool for studying dark matter and the universe's structure, with comprehensive theory and applications summarized in this review.
Contribution
This review provides a detailed derivation of gravitational lensing equations and summarizes current applications across various cosmic structures.
Findings
Derived equations of thin and extended gravitational lensing
Summarized lensing by stars, galaxies, and large-scale structures
Highlighted key results in dark universe analysis
Abstract
Gravitational lensing has developed into one of the most powerful tools for the analysis of the dark universe. This review summarises the theory of gravitational lensing, its main current applications and representative results achieved so far. It has two parts. In the first, starting from the equation of geodesic deviation, the equations of thin and extended gravitational lensing are derived. In the second, gravitational lensing by stars and planets, galaxies, galaxy clusters and large-scale structures is discussed and summarised.
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