Electromechanical oscillations are inherent to interconnected power systems. However, the frequency of the oscillations and the number of generators that oscillate in any electromechanical oscillatory mode depend on the structure of the power system network. Low frequency electromechanical oscillations occur when existing generation/load areas are connected to other similar areas by relatively weak transmission lines. Weak interconnections are obvious in many interconnected systems, for example, when two independent electric grids are interconnected for the first time through one or two tie lines. However, in systems that have been interconnected for some time, such as the US/Canadian interconnected systems, and that are being stressed by increased load, weak links are less obvious. Often, the first signs of trouble are low frequency oscillations becoming unstable. The connection between loading and stability is not always obvious. It is also unclear which contingencies may lead to oscillatory instability. This tutorial examines in detail the relationship between low frequency oscillations and weak interconnections in the transmission system network. The basis of the analysis is the observation that generators in specific areas of a power system behave coherently in low frequency oscillations and that groups of coherent generators are separated from other groups of coherent generators by weak interconnections. This observation is also the starting point for dynamic system reduction.