Vayikra/Leviticus 19:18
Lo-tikom velo-titor et-beney amecha ve’ahavta lere’acha kamocha ani YHVH.
You shall not take vengeance, nor bear any grudge against the children of your people; but you shall love your neighbor as yourself. I am the LORD.

The Talmud defines vengeance in this way:

Mishlei/Proverbs 20:22
Don’t say, "I will pay back evil." Wait for YHVH, and he will save you.

Mattityahu/Matthew 5:43-47
"You have heard that our fathers were told, ‘Love your neighbor—and hate your enemy.’ But I tell you, love your enemies! Pray for those who persecute you! Then you will become children of your Father in heaven. For he makes his sun shine on good and bad people alike, and he sends rain to the righteous and the unrighteous alike. What reward do you get if you love only those who love you? Why, even tax-collectors do that! And if you are friendly only to your friends, are you doing anything out of the ordinary? Even the Goyim do that!

It has been mistakenly taught that Jewish tradition teaches to hate your enemies. Actually, no such statement can be found in either the Bible or Rabbinic teaching. It was just recently found only in the teachings of the Dead Sea Sect. This does, however, prove that Yeshua was very much familiar with this sect.

In fact, the Sages teach the same as Yeshua:

Yeshua taught that instead of retailating, we are to pray for our enemies. Likewise, there is a medival Jewish work that states: "Pray for your enemy that he serve God." (Orchot Tzaddikim15c)

Matttiyahu/Matthew 5:38-42
"You have heard that our fathers were told, ‘Eye for eye and tooth for tooth.’ But I tell you not to stand up against someone who does you wrong. On the contrary, if someone hits you on the right cheek, let him hit you on the left cheek too! If someone wants to sue you for your shirt, let him have your coat as well! And if a soldier forces you to carry his pack for one mile, carry it for two! When someone asks you for something, give it to him; when someone wants to borrow some thing from you, lend it to him.

The Torah passage, "Ayin tachat ayin shen tachat shen" [Eye for an eye, and tooth for a tooth - Shemot/Exodus 21:24] is often misunderstood to show that the so called "Old Testament" teaches retailation instead of forgiveness of the "New Testament". But what Ayin tachat ayin actually teaches is that there should be limitations on punishments, and it should be appropriate for the crime. In its context, it is the judges that the punishment.

Romans 12:17-21
Repay no one evil for evil, but try to do what everyone regards as good. If possible, and to the extent that it depends on you, live in shalom with all people. Never seek revenge, my friends; instead, leave that to God’s anger; for in the Tanakh it is written, "YHVH says, ‘Vengeance is my responsibility; I will repay.’ [Devarim/Deuteronomy 32:35] " On the contrary, "If your enemy is hungry, feed him; if he is thirsty, give him something to drink. For by doing this, you will heap fiery coals of shame on his head." [Mishlei/Proverbs 25:21-22] Do not be conquered by evil, but conquer evil with good.

In The Artscroll Siddur there is a prayer at the end of the Shemoneh Esrei:

This prayer is asking YHVH's help in not responding in anger to those curse us. Instead of reacting to our emotions, we need to respond in accordance to the Torah, which teaches to love our neighbor as ourselves. In addition, we should leave it in His hands. In due time, he will recompense.

Shalom v'brakhot v'simcha,
Moreh Chizkiyah Shlomo (Carl)