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The objective of these lectures is to provide a practical introduction to strong gravitational lensing including the data, the theory, and the application of strong lensing to other areas of astrophysics. This is Part 2 of the complete Saas Fee lectures on gravitational lensing. Part 1 (Schneider 2004) provides a basic introduction, Part 2 (Kochanek 2004) examines strong gravitational lenses, Part 3 (Schneider 2004) explores cluster lensing and weak lensing, and Part 4 (Wambsganss 2004) examines microlensing. 1 The complete lectures provide an updated summary of the field from Schneider, Ehlers & Falco ([1992]). There are also many earlier (and shorter!) reviews of strong lensing (e.g. Blandford & Kochanek [1987a], Blandford & Narayan [1992], Refsdal & Surdej [1994], Wambsganss [1998], Narayan & Bartelmann [1999], Courbin, Saha & Schechter [2002], Claeskens & Surdej [2002]).

It is not my objective in this lecture to provide a historical review, carefully outlining the genealogy of every development in gravitational lensing, but to focus on current research topics. Part 1 of these lectures summarizes the history of lensing and introduces most of the basic equations of lensing. The present discussion is divided into 9 sections. We start in Section B.2 with an introduction to the observational data. In Section B.3 we outline the basic principles of strong lenses, building on the general theory of lensing from Part 1. In Section B.4 we discuss modeling gravitational lenses and the determination of the mass distribution of lens galaxies. In Section B.5 we discuss time delays and the Hubble constant. In Section B.6 we discuss gravitational lens statistics and the cosmological model. In Section B.7 we discuss the differences between galaxies and clusters as lenses. In Section B.8 we discuss the effects of substructure or satellites on gravitational lenses. In Section B.9 we discuss the optical properties of lens galaxies and in Section B.10 we discuss extended sources and quasar host galaxies. Finally in Section B.11 we discuss the future of strong gravitational lensing.

It will be clear to readers already familiar with the field that these are my lectures on strong lensing rather than an attempt to achieve a mythical consensus. I have tried to make clear what matters (and what does not), what lensing can do (and cannot do) for astrophysics, where the field is serving the community well (and poorly), and where non-experts have understood the consequences (or have failed to do so). Doing so requires having definite opinions with which other researchers may well disagree. We will operate on the assumption that anyone who disagrees sufficiently violently will have an opportunity to wreak a horrible revenge at a later date by spending six months doing their own set of lectures.

1 For astro-ph users, the lectures should be referenced as: Kochanek, C.S., Schneider, P., Wambsganss, J., 2004, Gravitational Lensing: Strong, Weak & Micro, Proceedings of the 33rd Saas-Fee Advanced Course, G. Meylan, P. Jetzer & P. North, eds. (Springer-Verlag: Berlin). Back.

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