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The United States Supreme Court has directly considered the Second Amendment only four times.
In three of those -- US v. Cruikshank, 92 U.S. 542 (1875), Presser v. State of Illinois, 116 U.S. 252 (1886), Miller v. Texas, 153 U.S. 535 (1894) -- it dismissed any Second Amendment issues on the grounds that the Bill of Rights (Amendments 1-10) formed a bar solely on the Congress of the United States, not on the actions of the individual states. While portions of the Bill of Rights have since been incorporated (protected from state infringement via the 14th Amendment), the Second Amendment has not.
It took the National Firearms Act of 1934 to create a federal law that might permit the courts to actually visit the Second Amendment. That case was US v. Miller, 307 U.S. 174 (1939). The procedural details of the case are less than optimal. The federal trial court ruled that the charges against two bootleggers -- Jack Miller and Frank Layton -- for carrying an unregistered, sawed off shotgun violated their Second Amendment rights and released them. They disappeared, never to be seen in court again. By the time the case arrived at the Supreme Court, their attorney, working pro bono, decided that the joy of representing two missing, non-paying clients before the Supreme Court of the United States was less than the effort warranted and he didn't show up to argue the case, either.
Against that background, the court set the Second Amendment protection as "possession or use of a [weapon having] some reasonable relationship to the preservation or efficiency of a well regulated militia" and remanded the lower courts to make the determination. But with Miller and Young long gone, that determination was never made.
But, based on Miller, there is an extensive body of consistent lower court rulings and a repeated refusal by the Supreme Court to revisit the issue.
The lower courts, starting from Miller, have ruled that bars against private oownership of automatic weapons or even handguns are not violations of the Second Amendment, nor are restrictions againt the possession of any weapon by certain classes of people whose history indicates they may pose a threat to others society.