Eating the flesh of a living animal is forbidden. This teaches us to be sensitive to cruelty to animals. The negative laws were enforced at the Garden of Eden. Cursing the name of G-d is forbidden. Besides honoring and respecting G-d, we learn from this precept that our speech must be sanctified, as that is the distinctive sign that separated man from the animals.
Mankind is commanded to establish courts of justice and a just social order.
This is in order to enforce the first six laws and enact any other useful laws or customs. The following verse is a reference to the prohibition against murder. The following is an implicit reference to the prohibition against theft. It shows that permission is needed to take something that is not explicitly yours. The following verse implies the prohibition against blasphemy.