Counting sort
Counting sort sorts integers (or keys mapped to integers) in a known range ${0,\ldots,k}$ by counting occurrences, prefix-summing the counts into positions, then placing each record into an output array.
Time and space are $O(n + k)$. It is not a comparison sort, so it can beat $n \log n$ when $k = O(n)$. Done carefully (scan input backward into the cumulative positions) it is stable, which radix sort needs for digit passes.
Use when keys are small integers or bytes. Skip when $k$ is huge relative to $n$ or keys are arbitrary comparable objects.