Light curves are at the heart of Photometry. These are essentially a collection of magnitude observations over a period of time.

For different types of object (ex. Supernova, Asteroids, Exoplanets, RR Lyrae, etc) the light curve will have different features. As such, the analysis will be different for each.

Time-series analysis is the application of mathematical and statistical tests to any set of time-varying data in an attempt to: 1) quantify the variation itself, and 2) use that variation to learn something about the behavior of the system.

Ultimately, the goals of time-series analysis are to gain some physical understanding of the system under observation: what makes the system time variable, what makes this system similar to or different than other systems with similar variability, and so on. The other goal is to perhaps be able to predict future behavior; if not an exact prediction, then at least some quantification of the limits of the system.