Did Jesus abolish punishment?

Those people who misunderstand Jesus when He tells us to 'turn the other cheek' have a real problem.
Many liberals have attempted to use this quotation from the Sermon on the Mount against the death penalty, for example. Unfortunately, if you are taking these words and using them in this way, you may not restrict their usage.
Clearly, it would then have to mean that this is extended to all punishments. In similar fashion, the story of 'The Woman taken in adultery' may not be used for extrapolation either as this would also mean that all punishments are to be ignored - [I shall deal with that issue on another occasion.]
Everything must be seen in the light of Matthew 5:17 where Jesus says "I have not come to abolish the Law." In chapter 5, verse 38 Jesus also says: "You have heard that it was said 'eye for eye and tooth for tooth' but I tell you, do not resist an evil person."
There is no contradiction here if you grasp the very simple, general principle that Jesus is speaking to His disciples, followers and future Christians. He explains how Christians must not act by taking revenge. The 'eye for eye' principle was not designed for personal vengeance and vengeance is always personal.
No. Jesus has not abolished the principle of the Lex Talionis; balanced punishment. That is the domain of Society and not the individual. The use of 'eye for eye' is for social retribution and never personal revenge. Retribution can never be personal; it is always neutral.
To a large extent, The Old Testament is about how to run a society and The New is about how to run your own life. It is the only way that the Scriptures may be interpreted - otherwise they are contradictory which is clearly not the case.