for (int i = 0; i < list.Length-1; i++)
{
    for (int j= i+1; j< list.Length; j++)
    {
        if (list[i] > list[j])
        {
                list.Swap(i, j);
        }
    }


}

bool swappedThisPass;
for (int i = 0; i < list.Length - 1; i++)
{
    swappedThisPass = false;
    for (int j = list.Length -1; j>i; j--)
    {
        if (list[j-1] > list[j])
        {
            swappedThisPass = true;
            list.Swap(j-1, j);
        }
    }
    if (swappedThisPass == false) break;
}

for (int i = 1; i < list.Length; i++)
{
    int j = i;
    while (j > 0 && list[j - 1] > list[j])
    {
        list.Swap(j-1, j);
        j--;
    }
}

Basic insertion sort. Given a string like 'FEDCBA' performance is as bad as bubble sort, but real world is just as good. Improvement is we make better use of the face we know that once one comparision returns 'no swap required' nothing to the left of us does either.

for (int i = 0; i < list.Length; i++)
{
    int minIndex = i;
    for (int j = i + 1; j < list.Length; j++)
    {
        if (list[j] < list[minIndex]) minIndex = j;
    }
    list.Swap(i, minIndex);
}

Basic selection sort. While the number of reads is as bad as bubble sort, the number of writes is far fewer. In the example below, only the final green in a sequenece is an actual swap.