  We investigate several aspects of the Assouad dimension and the lower
dimension, which together form a natural `dimension pair'. In particular, we
compute these dimensions for certain classes of self-affine sets and
quasi-self-similar sets and study their relationships with other notions of
dimension, like the Hausdorff dimension for example. We also investigate some
basic properties of these dimensions including their behaviour regarding unions
and products and their set theoretic complexity.
