When we look at a binary string, finite or infinite, we may have some kind of intuition about how difficult it would be to describe. For instance, a string composed of all 0's would be easy to describe, but a typical string generated by flipping a coin wouldn't be. One of the mathematical tools we use to measure this aspect of a binary string is Kolmogorov complexity. In this project, we'll study variants of Kolmogorov complexity that measure how difficult it is to describe a given finite binary string in different ways. Some group members will be looking at how these variants are related to each other, and some will be looking at using a single variant to compare the complexities of infinite binary strings.