Abstract
Strong lensing at the galaxy scale is useful for numerous applications in
Astrophysics and Cosmology. Some of the principal applications are studying the
mass structure, formation, and evolution of elliptical galaxies, constraining
the stellar initial mass function, and measuring cosmological parameters. Since
the first discovery of a galaxy-scale strong lens in the eighties, this field
has come a long way regarding data quality and techniques to model the data. In
this review article, we describe the most common methodologies to model lensing
observables of galaxy-scale strong lenses, especially the imaging data, as it
is the most available and informative source of lensing observables. We review
the main results from the literature in astrophysical and cosmological
applications of galaxy-scale strong lenses. We also discuss the current
limitations of the data and methodologies and provide a future outlook of the
expected development and improvements in both aspects in the near future.
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