There have been some university courses which influenced me a lot, namely Explorative Data Analysis ("KDD / Data Mining / TDM / Neuronal Networks") and Applied Mathematics (Numerics / Statistics).
A time series is a collection of data which is labeled with time stamps. There are lot of interesting tasks which can be done with them, e.g. finding a compact description, filtering, analyzing for certain shapes, forecasting or comparison.
At a seminar I checked out a technique that is called Dynamic Time Warping (DTW), that is about comparing and finding similar time series with compressing and stretching operations. It's a computionally expensive method which utilizes Dynamic Programming and has in its basic variant quadratic time and space complexity. Mainly Prof Keogh found some interesting improvements of that drawback. My compilation of this topic with a flavor of bioinformatics can be found here.
This is an art of combining serveral techniques from diverse fields, naming Statistics, Data Mining, Machine Learning together with appropriate visualization techniques for structuring data with the goal to understand and represent relevant Information (Knowledge).
A very interesting and at the same time simple technique is the self-organizing map. That is a neuronal network which is capable of projecting high-dimensional data into a lower dimensional dataspace with a non-linear fashion while preserving topology to a certain degree.
A growing interest at current is the development of interactive information visualization techniques.