Martin Strömqvist: What is uniform distribution mod 1?

The theory of uniform distribution mod 1 involves many mathematical disciplines such as number theory, analysis, dynamical systems and probability. It was initiated by Hermann Weyl in the early 20th century. I will start from the beginning and cover a few basic results from uniform distribution. Further investigation of the distribution of a sequence leads to the notion of discrepancy, which is a measure of the lack of uniformity of a sequence.