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Bubble sort (compare two elements and switch them if one of them is higher than other, depending on ordering preference), iterate over the whole array of elements. Efficency O(n^{2}).

Insert sort, make a separate list, where you insert the elements in an ordered manner, that is start at the smallest element and go until an element that is bigger than the input or end of list and insert it before that. Efficency O(n^{2}).

Selection sort, iterate over the whole array and find the smallest element, put it into start, then iterate from smallest +1, then smallest +2. Efficency O(n^{2}).

Merge sort, split array into smaller arrays until size 1 is reached, then assume size 1 is sorted, then merge them while sorting, the sub arrays. Efficency O(n logn).

Quicksort. Select a pivot point, split all elements that are larger than that to one side, smaller to other, then put the pivot, where it belongs. After do it on smaller arrays, when all is done, the arrays are merged and the final array is sorted. Efficency O(n logn).