| Introduction to Gravitational Lensing and Cosmology | p. 1 |
| Introduction | p. 1 |
| History of Gravitational Light Deflection | p. 2 |
| Discoveries | p. 5 |
| What is Lensing Good for? | p. 14 |
| Gravitational Lens Theory | p. 18 |
| The Deflection Angle | p. 18 |
| The Lens Equation | p. 20 |
| Magnification and Distortion | p. 23 |
| Critical Curves and Caustics, and General Properties of Lenses | p. 25 |
| The Mass-Sheet Degeneracy | p. 29 |
| Simple Lens Models | p. 31 |
| Axially Symmetric Lenses | p. 31 |
| The Point-Mass Lens | p. 34 |
| The Singular Isothermal Sphere | p. 36 |
| Non-Symmetric Lenses | p. 38 |
| The Cosmological Standard Model I: The Homogeneous Universe | p. 44 |
| The Cosmic Expansion | p. 44 |
| Distances and Volumes | p. 49 |
| Gravitational Lensing in Cosmology | p. 52 |
| Basics of Lensing Statistics | p. 54 |
| Cross-Sections | p. 55 |
| Lensing Probabilities; Optical Depth | p. 57 |
| Magnification Bias | p. 58 |
| The Cosmological Standard Model II: The Inhomogeneous Universe | p. 61 |
| Structure Formation | p. 61 |
| Halo Abundance and Profile | p. 71 |
| The Concordance Model | p. 77 |
| Challenges | p. 81 |
| Final Remarks | p. 83 |
| References | p. 84 |
| Strong Gravitational Lensing | p. 91 |
| Introduction | p. 91 |
| An Introduction to the Data | p. 92 |
| Basic Principles | p. 97 |
| Some Nomenclature | p. 98 |
| Circular Lenses | p. 101 |
| Non-Circular Lenses | p. 112 |
| The Mass Distributions of Galaxies | p. 121 |
| Common Models for the Monopole | p. 125 |
| The Effective Single Screen Lens | p. 129 |
| Constraining the Monopole | p. 130 |
| The Angular Structure of Lenses | p. 136 |
| Constraining Angular Structure | p. 140 |
| Model Fitting and the Mass Distribution of Lenses | p. 143 |
| Non-Parametric Models | p. 150 |
| Statistical Constraints on Mass Distributions | p. 152 |
| Stellar Dynamics and Lensing | p. 158 |
| Time Delays | p. 163 |
| A General Theory of Time Delays | p. 165 |
| Time Delay Lenses in Groups or Clusters | p. 169 |
| Observing Time Delays and Time Delay Lenses | p. 170 |
| Results: The Hubble Constant and Dark Matter | p. 174 |
| The Future of Time Delay Measurements | p. 181 |
| Gravitational Lens Statistics | p. 182 |
| The Mechanics of Surveys | p. 182 |
| The Lens Population | p. 185 |
| Cross Sections | p. 192 |
| Optical Depth | p. 193 |
| Spiral Galaxy Lenses | p. 196 |
| Magnification Bias | p. 197 |
| Cosmology With Lens Statistics | p. 205 |
| The Current State | p. 206 |
| What Happened to the Cluster Lenses? | p. 210 |
| The Effects of Halo Structure and the Power Spectrum | p. 216 |
| Binary Quasars | p. 218 |
| The Role of Substructure | p. 221 |
| Low Mass Dark Halos | p. 230 |
| The Optical Properties of Lens Galaxies | p. 232 |
| The Interstellar Medium of Lens Galaxies | p. 238 |
| Extended Sources and Quasar Host Galaxies | p. 243 |
| An Analytic Model for Einstein Rings | p. 243 |
| Numerical Models of Extended Lensed Sources | p. 248 |
| Lensed Quasar Host Galaxies | p. 251 |
| Does Strong Lensing Have a Future? | p. 255 |
| References | p. 256 |
| Weak Gravitational Lensing | p. 269 |
| Introduction | p. 269 |
| The Principles of Weak Gravitational Lensing | p. 272 |
| Distortion of Faint Galaxy Images | p. 272 |
| Measurements of Shapes and Shear | p. 274 |
| Tangential and Cross Component of Shear | p. 277 |
| Magnification Effects | p. 280 |
| Observational Issues and Challenges | p. 281 |
| Strategy | p. 282 |
| Data Reduction: Individual Frames | p. 284 |
| Data Reduction: Coaddition | p. 288 |
| Image Analysis | p. 292 |
| Shape Measurements | p. 295 |
| Clusters of Galaxies: Introduction, and Strong Lensing | p. 298 |
| Introduction | p. 298 |
| General Properties of Clusters | p. 299 |
| The Mass of Galaxy Clusters | p. 301 |
| Luminous Arcs and Multiple Images | p. 304 |
| Results from Strong Lensing in Clusters | p. 309 |
| Mass Reconstructions from Weak Lensing | p. 315 |
| The Kaiser-Squires Inversion | p. 316 |
| Improvements and Generalizations | p. 317 |
| Inverse Methods | p. 324 |
| Parameterized Mass Models | p. 327 |
| Problems of Weak Lensing Cluster Mass Reconstruction and Mass Determination | p. 330 |
| Results | p. 333 |
| Aperture Mass and Other Aperture Measures | p. 343 |
| Mass Detection of Clusters | p. 346 |
| Cosmic Shear - Lensing by the LSS | p. 355 |
| Light Propagation in an Inhomogeneous Universe | p. 356 |
| Cosmic Shear: The Principle | p. 358 |
| Second-Order Cosmic Shear Measures | p. 360 |
| Cosmic Shear and Cosmology | p. 366 |
| E-Modes, B-Modes | p. 371 |
| Predictions; Ray-Tracing Simulations | p. 377 |
| Large-Scale Structure Lensing: Results | p. 382 |
| Early Detections of Cosmic Shear | p. 383 |
| Integrity of the Results | p. 384 |
| Recent Cosmic Shear Surveys | p. 386 |
| Detection of B-Modes | p. 392 |
| Cosmological Constraints | p. 394 |
| 3-D Lensing | p. 397 |
| Discussion | p. 400 |
| The Mass of, and Associated with Galaxies | p. 404 |
| Introduction | p. 404 |
| Galaxy-Galaxy Lensing | p. 405 |
| Galaxy Biasing: Shear Method | p. 416 |
| Galaxy Biasing: Magnification Method | p. 427 |
| Additional Issues in Cosmic Shear | p. 430 |
| Higher-Order Statistics | p. 430 |
| Influence of LSS Lensing on Lensing by Clusters and Galaxies | p. 436 |
| Concluding Remarks | p. 439 |
| References | p. 442 |
| Gravitational Microlensing | p. 453 |
| Lensing of Single Stars by Single Stars | p. 454 |
| Brief History | p. 454 |
| Theoretical Background | p. 454 |
| How Good is the Point Lens - Point Source Approximation? | p. 458 |
| Statistical Ensembles | p. 460 |
| Binary Lenses | p. 461 |
| Theory and Basics of Binary Lensing | p. 462 |
| First Microlensing Lightcurve of a Binary Lens: OGLE-7 | p. 466 |
| Binary Lens MACHO 1998-SMC-1 | p. 467 |
| Binary Lens MACHO 1999-BLG-047 | p. 471 |
| Binary Lens EROS BLG-2000-005 | p. 472 |
| Microlensing and Dark Matter: Ideas, Surveys and Results | p. 475 |
| Why We Need Dark Matter: Flat Rotation Curves (1970s) | p. 475 |
| How to Search for Compact Dark Matter (as of 1986) | p. 477 |
| Just Do It: MACHO, EROS, OGLE et al. (as of 1989) | p. 477 |
| "Pixel"-Lensing: Advantage Andromeda! | p. 478 |
| Current Interpretation of Microlensing Surveys with Respect to Halo Dark Matter (as of 2004) | p. 479 |
| Microlensing toward the Galactic Bulge | p. 484 |
| Microlensing Surveys in Search of Extrasolar Planets | p. 486 |
| How Does the Microlensing Search for Extrasolar Planet Work? The Method | p. 486 |
| Why Search for Extrasolar Planets with Microlensing? - Advantages and Disadvantages | p. 488 |
| Who is Searching? The Teams: OGLE, MOA, PLANET, MicroFUN | p. 492 |
| What is the Status of Microlensing Planet Searches so far? The Results | p. 493 |
| When will Planets be Detected with Microlensing? The Prospects | p. 496 |
| Note Added in April 2004 (About One Year after the 33rd Saas Fee Advanced Course) | p. 497 |
| Summary | p. 497 |
| Higher Order Effects in Microlensing: | p. 499 |
| Astrometric Microlensing | p. 516 |
| Quasar Microlensing | p. 520 |
| Microlensing Mass, Length and Time Scales | p. 521 |
| Early and Recent Theoretical Work on Quasar Microlensing | p. 524 |
| Observational Evidence for Quasar Microlensing | p. 526 |
| Quasar Microlensing: Now and Forever? | p. 534 |
| References | p. 536 |
| Index | p. 541 |
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