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Article Contents

ABSTRACT

1.INTRODUCTION AND HISTORICAL PERSPECTIVE

2.LENSING THEORY AS APPLIED TO CLUSTERS OF GALAXIES
2.1.General description
2.2.Gravitational Lens Equation
2.3.Gravitational Lens Mapping
2.4.Critical and caustic lines
2.5.Multiple-images
2.5.1.Definition
2.5.2.Multiple-image symmetry
2.5.3.Examples of multiple-image systems
2.5.4.Multiple-image identification
2.5.5.Multiple-image regions
2.6.First order shape deformations - Shear
2.7.Mass-sheet degeneracy
2.8.Higher order shape deformations - Flexion

3.CONSTRAINING CLUSTER MASS DISTRIBUTIONS
3.1.Strong lensing modeling
3.1.1.Modeling approaches
3.1.2.From simple to more complex mass determinations
3.1.3.Modeling the various cluster mass components
3.1.4.Bayesian modeling
3.2.Probing the radial profile of the mass in cluster cores
3.3.Non-Parametric Strong Lensing modeling
3.4.Cluster Weak lensing modeling
3.4.1.Weak lensing observations
3.4.2.Galaxy shape measurement
3.4.3.From galaxy shapes to mass maps
3.4.4.Measuring total mass and mass profiles
3.5.Cluster Triaxiality

4.MASS DISTRIBUTION OF CLUSTER SAMPLES
4.1.Early Work
4.2.On-going and future cluster lensing surveys
4.3.Targeted cluster surveys
4.3.1.The Local Cluster Substructure Survey (LoCuSS)
4.3.2.The MAssive Cluster Survey
4.3.3.ESO distant cluster survey
4.3.4.Red-sequence cluster surveys
4.3.5.The Multi-Cluster Treasury: CLASH survey
4.4.Cluster lenses in wide cosmological surveys
4.4.1.The Sloan Digital Sky Survey
4.4.2.The CFHT-Legacy Survey
4.4.3.The COSMOS Survey

5.CLUSTER LENSES AS NATURE'S TELESCOPES
5.1.Magnification due to Gravitational Lensing
5.2.Cosmic Telescope Surveys
5.3.“Lens redshift” measurement
5.4.Lensing Surveys in the Sub-millimeter
5.5.Mid-Infrared Lensing Survey
5.6.Lensed Extremely Red Objects
5.7.Lensed Lyman-a Emitters
5.7.1.Spectroscopic critical line mapping
5.7.2.Narrow-band searches
5.8.Lyman-break Galaxies
5.9.Far Infra-Red Lensing Surveys
5.10.Cluster Lensed Supernovae

6.COSMOLOGICAL CONSTRAINTS FROM CLUSTER LENSING
6.1.Cosmography with multiple-images
6.2.Arc statistics and Primordial Non-gaussianity
6.3.Triplet statistics

7.COMPARISON OF OBSERVED LENSING CLUSTER PROPERTIES WITH THEORETICAL PREDICTIONS
7.1.Internal structure of cluster halos
7.2.Mass function of substructure in cluster halos
7.3.Dynamical evolution of cluster halos
7.4.Constraints on the nature of dark matter

8.FUTURE PROSPECTS

APPENDIX A: PARAMETRIC MASS DISTRIBUTIONS USED TO MODEL CLUSTERS
A.1.The Singular Isothermal Sphere
A.2.Truncated Isothermal Distribution with a Core
A.3.The Navarro-Frenk-White Model
A.4.Flexion for the Singular Isothermal Sphere

REFERENCES