1 Introduction. - 1. 1. Introduction. - 1. 2. Preview of Coming Attractions. - 1. 3. The Ordinary Hall Effect. - 1. 4. Measuring the Conductance. - 1. 5. Introduction to the Quantum Case. - 1. 6. Impurity Effects. - 1. 7. Gauge Arguments. - 1. 8. Inversion Layers. - 1. 9. Acknowledgements. - 1. 10. Notes. - 1. 11. Problems. - A The Integer Effect. - 2 Experimental Aspects and Metrological Applications. - 3 Effects of Imperfections and Disorder. - 4 Topological Considerations. - 5 Field Theory Scaling and the Localization Problem. - B: The Fractional Effect. - 6 Experimental Aspects. - 7 Elementary Theory: The Incompressible Quantum Fluid. - 8 The Hierarchy of Fractional States and Numerical Studies. - 9 Collective Excitations. - C: The Quantum Hall Effect. - 10 Summary Omissions and Unanswered Questions. - Appendix Recent Developments. - A. 1. Introduction. - A. 2. Off-Diagonal Long-Range Order. - A. 3. Ring Exchange Theories. - A. 5. Even-Denominator and Spin-Reversed States. - A. 6. Spin-Reversed Hierarchy. - A. 7. Summary andConclusions. - References. Language: English