Short English text: please check for my mistakes

Hi,
the following text is a summary I've prepared in order to help my younger cousin (he has an exam next week so he needs my support).

Thank you for your help
Luca
"The German expansion spread over Europe in the 1930s, probably as a reaction to the severe peace terms forced on Germany by the Allies. In 1920, the Allies had created the League of Nations, with the purpose to promote the cooperation between its members, but in 1935, when Italy invaded Abyssinia, which was a member of the League, the other members (notably Britain and France) decided not to act: this decision, taken with the purpose to win Italy's cooperation against Hitler, was interpreted as a sign of weakness by the Axis forces (Italy and Germany and Japan) and for the next four years, they took advantage of this state of things to seize new territories.
In 1938, the British prime Minister accepted the takeover of German-speaking parts of Czechoslovakia by Germany, after Hitler's written promise that Germany had no more territorial ambitions: six months later Germany occupied the rest of Czechoslovakia.
The year after, Germany invaded Poland and Britain, which was supporting the latter, was constrained to enter the war.
In May 1940 the German army attacked, defeating the French and driving the British army into the sea, with the latter saved by thousands of private boats at Dunkirk. The war, begun as a European struggle, spread worldwide when Germany attacked the Soviet Union and Japan attacked the United States.

Italy surrendered quickly in 1943; the year after, Britain and the USA invaded German-occupied France, starting to bomb German towns; in May 1945 Germany finally surrendered. In order to avoid further victims among their troops, the Allied used the new atomic bomb to defeat Japan, which surrendered soon later"