What was the Purpose of the Plagues?

The first three plagues were designed to establish the existence of God; they were introduced by the warning: "you shall know that I am God." Please note that it is only during the first three plagues that the חרטומים are involved. After the third plague when the חרטומים declare it is the finger of God, they are no longer involved as Hashem's existence is no longer under debate.

The second group of plagues was to demonstrate God's providence; here the introduction is: "you shall know that I am God in the midst of the land". This group is meant to prove that not only does God exist, but He is involved in the land and in worldly, human affairs, and that He watches over those who fear Him. This set of plagues highlights the distinction - as yet unmentioned - between the Egyptians and Bnei Yisrael. Only the Egyptians would be affected by these plagues.

The third group, finally, was to show the truth of prophecy; in connection with this group the Torah speaks of those who would not listen to God's word (Shemot 9:21) and ‘in order that you will know that there is none like Me in all the land’. Two messages have been conveyed so far to the Egyptians - the existence of God, and His guidance over the world. Now the time has come to express another message: the uniqueness of God. The third group of plagues gives special expression to the idea that God is the only God, for His actions are without precedent in anything that has ever happened in the world.