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2009 TASI Lecture -- Introduction to Extra Dimensions

We give a brief introduction to theories with extra dimensions. We first introduce the basic formalism for studying extra-dimensional theories, including the Kaluza-Klein decomposition and the effective theory for 3-branes. We then focus on two types of scenarios: large extra dimensions as a solution to the hierarchy problem and TeV$^{-1}$-size extra dimensions with Standard Model fields propagating in them. We discuss the experimental tests and constraints on these scenarios, and also the questions in particle physics which may be addressed with the help of extra dimensions. This is the write-up of the lectures given at the 2009 TASI summer school. Other interesting topics such as warped extra dimensions are covered by other lecturers.