The brief is just from the city asking the court to overturn the lower courts ruling.
Just a little bit of there summary, one of the arguments is that the 2nd only applies to the Militia.
1. The text and history of the Second Amendment conclusively refute the notion that it entitles individuals to have guns for their own private purposes. In-stead, it protects the possession and use of guns only in service of an organized militia.
The first clause—“[a] well regulated Militia, being necessary to the security of a free State”—speaks only of militias, with not a hint about private uses of fire-arms. A well-regulated militia is the antithesis of an unconnected group of individuals, each choosing unilaterally whether to own a firearm, what kind to own, and for what purposes.
The second clause—“the right of the people to keep and bear Arms, shall not be infringed”—equally ad-dresses the possession and use of weapons in connection with militia service. In 1791, “Arms” and “bear Arms” were military terms describing the use of weapons in the common defense, and the word “keep” was used in connection with militiamen’s possession of the arms necessary for militia service.
Taken together, the two clauses permit only a militia related reading. To conclude that the Framers in-tended to protect private uses of weapons, the majority below read the entire first clause to be extraneous and the second to be in tension with the natural, military meaning of “bear Arms.” If that had been the Framers’ intent, they would have omitted the first clause and used non-military language in the second.