I guess you could say that Germany (the home nation for the Nazi Party) was the first country taken over by the Nazis. Next would come Austria in 1936 & Czechoslovakia in 1938 before the war began. Then with the start of the war: Poland in 1939. Other countries were defeated & conquered in 1940 & 1941.
To seize territory, they used the German army, the Wehrmacht. To control the occupied countries, they had to mainly rely on the cooperation and obedience of the Civil Services of those countries, which almost everywhere was not much of a problem. In most countries the Nazis installed units of the SS and the Gestapo to 'help' with police duties and in all occupied countries they kept Wehmacht and/or Waffen-SS units. The role of 'head of…
The first territories outside peninsular Italy that Rome acquired were western Sicily, Sardinia and Corsica. They were taken over from the Carthaginians after the First Punic War. The first territory acquired outside present day Italy, apart from Corsica, was southern Spain. It was taken over from the Carthaginians after the Second Punic War.
Prior to 1948, the territory that is now Israel was the British Mandate of Palestine. Britain had taken over the mandated territory from the former colonial power, Turkey, following the First World War and was close to granting independence to the Palestinians when the Jews decided to resolve matters in their own favour.
They were on the Nazis side like Italy so the Nazis didn't need to invade it. Sweden wasn't officially an axis country, they just helped the Nazis a lot in exchange for a lot of money. That's why Sweden is so rich today. If the Nazis had invaded, there would've been terrorism and they wouldn't have gotten as much resources from Sweden.