in addition to @Ronak Shah answer you can also use arrange of dplyr.
It looks a bit simpler to me.
arrange(DataTable,Age,Name)
gives
Name Age Grade
1 Alex 16 3
2 Jeff 16 2
3 Michi 16 4
4 Rodger 16 2
5 Nelle 17 1
6 Alex 18 5
7 Thomas 18 4
Here, it first sorts by Age then Name and you can add more variables so on.