Notes on random reals

The theory of random real numbers is exceedingly well-developed, and fascinating from many points of view. It is also quite challenging mathematically. The present notes are intended as no more than a gateway to the larger theory. They review just the most elementary part of the theory (bearing on Kolmogorovand Martin-Löf-randomness). We hope that the simple arguments presented here will encourage the enterprising student to examine richer treatments of the subject available elsewhere, notably, in Downey and Hirschfeldt (2010).1 Comments and corrections to the notes are, of course, welcome.