ABSTRACT
There have been a number of excellent expositions of the theory of uniformly distributed sequences; to name but two, the ground-breaking work [43] of Weyl and the encyclopedic volume [23] of Kuipers and Niederreiter. I propose to present some recent results in the theory. For the most part, I have included only those topics on which I have something original to say. I also develop in parallel a theory of sequences that are as far from uniformly distributed as possible.
