  Simple aerodynamic configurations under even modest conditions can exhibit
complex flows with a wide range of temporal and spatial features. It has become
common practice in the analysis of these flows to look for and extract
physically important features, or modes, as a first step in the analysis. This
step typically starts with a modal decomposition of an experimental or
numerical dataset of the flow field, or of an operator relevant to the system.
We describe herein some of the dominant techniques for accomplishing these
modal decompositions and analyses that have seen a surge of activity in recent
decades. For a non-expert, keeping track of recent developments can be
daunting, and the intent of this document is to provide an introduction to
modal analysis that is accessible to the larger fluid dynamics community. In
particular, we present a brief overview of several of the well-established
techniques and clearly lay the framework of these methods using familiar linear
algebra. The modal analysis techniques covered in this paper include the proper
orthogonal decomposition (POD), balanced proper orthogonal decomposition
(Balanced POD), dynamic mode decomposition (DMD), Koopman analysis, global
linear stability analysis, and resolvent analysis.
