At our next meeting on 28th November we will discuss the P vs. NP problem of complexity theory presented by Thomas Zauner. There are several levels of readings.
Watch this video explaining the basics about the P vs. NP problem and complexity theory.
Read this article explaining not only the concepts, but also shedding some light on recent developments in research.
Watch these excellent and well explained lecture video on an introduction complexity.
(For further studies see: https://www.youtube.com/watch?v=eHZifpgyH_4)
For further reading consult the always-insightful Stanford encyclopedia of philosophy.