More about jumps
This one is called Two Points Up (or Niken tobi).
Although it will give you greater influence over the board , it is easier to be cut by the enemy since there is a larger space between the stones (points 1 and 2).
There is also the Three Stitches Up and Four Stitches Up.
These big jumps are often used as early game moves.
This jump is called a Keima (Knight) move as in chess.
Knight moves are often used to enclose territory in the corners as shown on the left.
This is called a Kosumi - a diagonal move.
The two stones are virtually connected but it is a little slow as the extension of the fenced off of the first stone is smaller than that of the previous case.