The document discusses quicksort algorithms and provides pseudocode to sort a list of numbers. It shows the steps of choosing a pivot element, comparing elements on the left and right of the pivot, swapping elements if out of order, and recursively applying the process to subarrays until the full list is sorted. An example sort of the list [5, 3, 1, 9, 8, 2, 4, 7] is provided to demonstrate how the pivot element is used to partition the list into sorted left and right subarrays at each step.