Models with Extra Dimensions and Their Phenomenology

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The Arkani-Hamed-Dimopoulos-Dvali and the Randall-Sundrum models with extra spacelike dimensions, recently proposed as a solution to the hierarchy problem, are reviewed. We discuss their basic properties and phenomenological effects of particle interactions at high energies, predicted whithin these models.
52 pages, 15 postscript figures, LaTeX, based on the lectures given at the XI School "Particles and Cosmology" (Baksan, April 18-24, 2001); new references are added in the revised version

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