After the convertion to Christianity in the year 1000, laws were one of the first things written down in order to avoid disagreements. It's said that laws were first written in the winter of 1117–1118 at Hafliði Másson's farm at Breiðabólsstaður in Vesturhóp. The Commonwealth laws were later called Grágás and are preserved in some ancient manuscript formats and 2 parchments written in the final years of the Commonwealth period.
There have been Judges at the Alþing since its beginning, but around 960, four judges were appointed, one for each quarter of the country. Legal cases that had not been concluded at district meetings could be sent to a quarter judge at the Alþing. Then early in the 11th century, a fifth judge was appointed who sat in the Lögrétta and could take up cases quarter judges had left unfinished.
During the Commonwealth period power was in the hands of just a few individuals. When crimes were committed there was no central authority to carry out judgement or Thus there were no executions or indeed any other punishments carried out at Þingvellir during that time.
When Icelanders came under the authority of the Norwegian king, implementation of power was transferred to the king's authority figures, the district magistrates. In 1281 Jónsbók was approved as a book of law and became the basis for legal procedures in Iceland for the following centuries. It's said that no book in Iceland has been more widely read or more often learned by heart than Jónsbók.
In 1281, with the approval of Jónsbók, a book of law, and the transfer of judicial power to the Norwegian king's authority figures, punishments became more severe than they'd been during the Commonwealth period. With the legalisation of Stóridómur, the Great Judgement, in 1564, the frequency of corporal punishment at Þingvellir increased significantly. Place names such as Drowningpool, Gallowsrock and others, remain as a reminder of grimmer times.