Yes there were laws, seven to be exact as they are called the Noahic Commandments.
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Noahic (Noah) Commandments are seven commandments first given to Adam by God before the flood and brought to remembrance by God to Noah after the flood, which are now binding on both Jew and Gentile as there were no Jew or Gentile in the days of Noah, and none today on this side of the cross as we are all one in the Spirit of God, Galatians 3:28. Abraham was the first one to be called a Hebrew, Genesis 14:13, and until the days of Jacob there was no land called Israel or any laws pertaining to the rituals of the Temple, sacrifices, festivals, Torah, Kohanim and Levites, the King and the Nazarite as none of that existed yet. What there were was seven to begin with that are the laws that are written on our heart. Laws were added to as the generations grew until there became 613 that became a curse as no one could ever follow all of them.
Beginning with Genesis 2:16 the Babylonian Talmud listed six commandments given first to Adam and then again to Noah after the flood. The seven make up the first parts of the ten that God gave to Moses on Mt Sinai in Exodus 20. Below is a comparison list of the seven and the full ten which are all the first part of the 613 laws given to Moses as some were for the Hebrews pertaining to the rituals of the Temple, sacrifices, festivals, Torah, Kohanim and Levites, the King and the Nazarite and then there are the existing moral laws (commandments) for all, Jew and Gentile to follow that are written upon our heart. Christ did not come to destroy all the laws, but to fulfill the righteousness of the laws, Matthew 5:17-22.
Noahic Laws:
Not to worship idols.
Not to curse God.
To establish courts of justice.
Not to commit murder.
Not to commit adultery or sexual immorality.
Not to steal.
Not to eat flesh torn from a living animal.
Mt. Sinai Laws:
You shall have no other gods before Me.
You shall not make idols.
You shall not take the name of the LORD your God in vain.
Remember the Sabbath day, to keep it holy.
Honor your father and your mother.
You shall not murder.
You shall not commit adultery.
You shall not steal.
You shall not bear false witness against your neighbor.
You shall not covet.
Part of the ten laws broken down to various commands within one law:
Other gods and idols are as one not to worship, but broke down into two commands
Remember the Sabbath was added to the ten commandments by God as a remembrance of all God did in six days (Gods timing) and rested on the seventh, Genesis 2:1-3; Matthew 12:1-13
To establish courts of justice was only given to Noah for the new generations to come after the flood
Honor your father and mother was not given to Noah, but was added to the ten commandments by God as the generations grew.
Not to covet was added to the ten commandments by God, but broke down into seven commands as your neighbor's house; you shall not covet your neighbor's wife, nor his male servant, nor his female servant, nor his ox, nor his donkey, nor anything that is your neighbor's.