In order to understand in physical terms why the Sun exhibits oscillations at precisely defined frequencies, we consider in this chapter the oscillations in an idealized “star.” Specifically, we revert to the topic of polytropes (see Chapter 10), since these provide in certain cases an analytic form for the radial profile of pressure and density in which oscillations can occur. Of course, if we were undertaking a detailed examination of the Sun, we would have to make use of the full numerical radial profiles of pressure and density: but those numerical solutions make it more complicated to derive the properties of the oscillations. So in this first course in solar physics, we simplify the problem by considering the oscillation modes of a polytrope. Results from the polytropic case contain many of the important characteristics of oscillations in the “real Sun.”