World War II: 1939
World War II began when Nazi Germany under Adolf Hitler invaded Poland on September 1st, 1939. This invasion was under the false pretext that Poland had orchestrated a series of sabotage operations against German targets along the border. The reality is actually the opposite; German commandos had staged pretend raids so as to give a casus belli for their invasion of Poland. Hitler, using the supposed attacks by the Poles as his reasoning, invaded Poland.
The major tactical innovation of the war was the use of combined arms warfare, typified by the German doctrine of blitzkrieg. In this style of warfare armor, infantry, artillery and air power (see Luftwaffe) all coordinate to achieve overwhelming superiority at point on the enemy lines. Armor and fast-moving infantry units then exploit the gap and penetrate deep behind enemy lines. Slower moving foot infantry would follow behind the motorized (later mechanised) and armored forces, securing their flanks in order to prevent encirclement. The objective is to cause a widespread collapse of the enemy's ability to fight. It was particularly effective during the early and middle stages of the war, before the Allies developed effective countermeasures.
On September 17th, the Soviet Union invaded Poland. Stalin had secured a ceasefire with Japan over the Khalkhin Gol incidents, allowing him to follow up on his promise to invade Poland from the east, as per the Molotov-Ribbentrop Pact. The combined weight of German and Soviet forces sealed the inevitable. Poland surrendered on September 27th, following the fall of Warsaw. Remaining pockets of resistance were crushed and surrendered on October 6th.
Britain and France declared war on Germany two days after the invasion of Poland began. The Dominions of the British Commonwealth followed shortly after. Polish resistance would soon begin, and would continue throughout the entire war. Poland was divided between Germany and the USSR. Germany acquired the western regions, approximately 48.4% of the country. The Soviet Union acquired the rest. About 270 sq. miles of land was given to Germany's puppet state Slovakia.
Operation Himmler and the Gleiwitz incident
Operation Himmler was a false flag operation planned by the SS and SD to create the appearance of a Polish attack on Nazi Germany. In doing so, Nazi propaganda used the "attacks"" as justification to go to war with Poland. Heinrich Himmler was the architect of the plan, Reinhard Heydrich supervised the planning, and Heinrich Müller was the overall manager. Himmler had the approval of Hitler for the duration of the operation.
The Gleiwitz incident occurred on the night of August 31st. A small party of German operatives dressed in standard Polish uniforms took over the Gleiwitz radio station. They then began to broadcast an anti-German message in Polish. To make the attack seem more plausible, the Germans used human corpses evidence of the attack. Several prisoners of the Dachau concentration camp were brought to the site, drugged, and shot. 
That being said, the German invasion was not a surprise attack. The bridges of the Vistula River connecting German and Polish territory over which the invasion occurred, had already been fitted with demolition charges in August by the Poles, and in fact at sunrise on September 1, they did demolish a strategic bridge at Dirschau.
The day after the Gleiwitz incident occurred, the Wehrmacht invaded Poland. The Germans possessed a numerical advantage in every aspect. 2,400 tanks, mainly Panzer Is and IIs, were organized into 6 panzer divisions. Around 2,500 planes were used in the Polish campaign, the majority modern. At this time, the Luftwaffe was probably the most experienced air force in the world, thanks to its participation in the Spanish Civil War.
During the first few days of the invasion, the Germans made good progress, but casualties were high due to stiff Polish resistance. As the days went on, Polish resistance grew weaker and weaker. The Polish army didn't have an effective countermeasure to the revolutionary blitzkrieg, and many Polish divisions were encircled and destroyed. The Germans suffered 49,000 casualties compared to 199,700 total casualties for the Polish.
Soviet invasion from the east
Honoring the terms of the Molotov-Ribbentrop Pact, Stalin invaded from the east on September 17th. The relatively sparse Polish forces were easily swept aside by the Red Army. His forces were organized into two fronts, or army groups. At the end of the campaign, the Soviets had captured 99,000 Polish soldiers, at the cost of around 13,000 casualties.
- Christopher J. Ailsby, The Third Reich Day by Day, Zenith Imprint, 2001, ISBN 0-7603-1167-6, Google Print, p. 112
- James J. Wirtz, Roy Godson, Strategic Denial and Deception: The Twenty-First Century Challenge, Transaction Publishers, 2002, ISBN 0-7658-0898-6, Google Print, p.100
- Chant, Christopher (unk. date). "Operation Dirschau" Codenames website.