On Kolmogorov Complexity

This semester I assisted to a course on Kolmogorov Complexity and Minimum Description Length, given at the Institute for Logic, Language and Computation of the University of Amsterdam.
The main lecturer, Paul Vitanyi, is the c0-author of THE book on Kolmogorov Complexity. Peter Gr├╝nwald, invited professor in two lectures, is the author of THE book on the Miniumum Description Length principle. The exercise sessions were given by a talented PhD student of them, Wouter Koolen-Wijkstra.

But what is this all about?
In simple words, the Kolmogorov Complexity of a sequence of characters is the length of the shortest program that outputs that sequence. It is the theoretical limit of compression.