There are several different points that are made in the various answers.

1. Pharaoh at first hardened his own heart in order to withstand the earlier plagues. Once he had established the pattern, Hashem allowed him to continue in that pattern by hardening later to be able to resist the later plagues.

2. Hashem only strengthened Pharaoh so that he could make an independent decision at all times. That is, He was trying to allow Pharaoh to do the right thing of his own free will. Pharaoh refused to take advantage of that opportunity.

3. Pharaoh, by consistently refusing to send them out of his own free will, forfeited the ability to choose as the final punishment had been decreed. Once he reached that level of evil, he could not turn back.

See what I answer at What does it mean that God hardened Pharaoh’s heart?.

There are a number of answers ranging from strengthening Pharaoh so that he could withstand the plagues, to the difference in language showing that Pharaoh hardened his own heart at first and G0d only did that later after Pharaoh had reached the level of requiring punishment, ...

Check out Hardened Hearts: Some Explanations to see some of them Reinterpretation of the Term (Saadiah Gaon), The Modest Solution (Ramban), The Bold Claim: Pharaoh Acts Freely (Albo), Hardening as Punishment (Rambam)

Pharaoh's Heart goes into detail on the theme of Pharaoh having reached a level through his own free will in which this was an appropriate punishment.

An interesting point is that the word for 'harden' is actually 'heavy'. The Egyptian superstition was that when being judged after death, a person's heart was weighed against a feather (the feather of Truth IIRC). If the heart was lighter, he was judged innocent. Thus, Pharaoh hardening his own heart can mean that he was guilty even in terms of his own beliefs. Hashem hardening his heart can therefore mean that Pharaoh is now punished by those means or that his refusal (in his own terms) to repent causes him to lose the ability to repent, or by moving along the path of error he has that much farther to go to return, ...

Rav Shimshon Rafael Hirsch prefers the idea that Hashem helped strengthen Pharaoh so that he had free will and could make a totally objective decision. He prefers the meaning to be 'strengthen' rather than 'harden'.

Also note @Fred giving the pointers

Also, for some examples of articles that discuss some of the major views among the rishonim on this, see here, here, here, and here

Each time his heart was hardened was a different situation. Each plague needed to have his heart strengthened individually. It is not that the torah says it twenty times for one case. Thus the torah needs to repat the phrase each time he must do it or when Hashem does it for him.

There are several different points that are made in the various answers.

1. Pharaoh at first hardened his own heart in order to withstand the earlier plagues. Once he had established the pattern, Hashem allowed him to continue in that pattern by hardening later to be able to resist the later plagues.

2. Hashem only strengthened Pharaoh so that he could make an independent decision at all times. That is, He was trying to allow Pharaoh to do the right thing of his own free will. Pharaoh refused to take advantage of that opportunity.

3. Pharaoh, by consistently refusing to send them out of his own free will, forfeited the ability to choose as the final punishment had been decreed. Once he reached that level of evil, he could not turn back.

See what I answer at What does it mean that God hardened Pharaoh’s heart?.

There are a number of answers ranging from strengthening Pharaoh so that he could withstand the plagues, to the difference in language showing that Pharaoh hardened his own heart at first and G0d only did that later after Pharaoh had reached the level of requiring punishment, ...

Check out Hardened Hearts: Some Explanations to see some of them Reinterpretation of the Term (Saadiah Gaon), The Modest Solution (Ramban), The Bold Claim: Pharaoh Acts Freely (Albo), Hardening as Punishment (Rambam)

Pharaoh's Heart goes into detail on the theme of Pharaoh having reached a level through his own free will in which this was an appropriate punishment.

An interesting point is that the word for 'harden' is actually 'heavy'. The Egyptian superstition was that when being judged after death, a person's heart was weighed against a feather (the feather of Truth IIRC). If the heart was lighter, he was judged innocent. Thus, Pharaoh hardening his own heart can mean that he was guilty even in terms of his own beliefs. Hashem hardening his heart can therefore mean that Pharaoh is now punished by those means or that his refusal (in his own terms) to repent causes him to lose the ability to repent, or by moving along the path of error he has that much farther to go to return, ...

Rav Shimshon Rafael Hirsch prefers the idea that Hashem helped strengthen Pharaoh so that he had free will and could make a totally objective decision. He prefers the meaning to be 'strengthen' rather than 'harden'.

Also note @Fred giving the pointers

Also, for some examples of articles that discuss some of the major views among the rishonim on this, see here, here, here, and here