World War II began in Europe on September 1, 1939, when Germany invaded Poland. Great Britain and France responded by declaring war on Germany on September 3. The war between the U.S.S.R. and Germany began on June 22, 1941, with the German invasion of the Soviet Union.
World War II is generally considered to have begun on 1 September 1939, with the invasion of Poland by Germany and subsequent declarations of war on Germany by the United Kingdom and France on the 3rd.