Typical ones are: O(n^2) or O(nlogn) or O(n), for more check Big-O Cheatsheet.
Strictly an in-place sort needs only o(1) memory beyond the items being sorted.
So an in place algorithm does not need any extra memory.
Some sorting algorithms are implemented in a recursive manner, especially the divide and conquer ones. Such as merge sort and quick sort.
Stable sorting algorithms maintain the relative order of records with equal values.