Hitler intended to conquer Russia for 'living space'. To prevent France attacking Germany while he did so he decided to knock France out of the war first.

So on May 1940 he launched an invasion of Holland, Belgium and France. Its success was largely due to the German strategic plan, devised by General von Manstein, who suggested that the main thrust of the attack should come where the Allies least expected it-through the Ardennes Hills. This wooded, hilly country was thought to be too difficult for armoured columns. At a private dinner Manstein persuaded Hitler to press the German High Command to adopt the plan. The aim was to split the allied armies by thrusting straight for the English Channel.

Of the 2700 German tanks, army Group 'A', which led the main attack, in 7 panzer divisions, had 2000 tanks: a massive concentration of armour. The Allies had about the same number of tanks but made the mistake of spreading them among the infantry. The Germans had twice as many aircraft and an effective signalling system through which the panzers' divisions could quickly call up help from aircraft.

Army Group 'B's' attack to the north was made with much less armour. Paratroops and troops in gliders made landings in Holland and Belgium and soon broke through the river defences. Rotterdam was severely bombed and Holland was conquered in five days. French troops and the British Expeditionary Force (BEF) made their planned advances into Belgium, thinking they were facing the main German attack. The mass of German tanks in Army Group 'A' struck through the Ardennes (10-13 May). The River Meuse was a major obstacle but panzer infantry crossed the river in inflatable rubber dinghies and engineers built floating bridges for tanks and vehicles, while guns fired at the French defenders. Guderian, commanding the German forces on the left, crossed at Sedan. Generals Hoth and Rommel, leading troops on the right, crossed near Namur. The French troops stationed opposite the Ardennes were poorly trained and the German Stuka dive-bombing shattered their nerves. At Sedan they mistook their own tanks for the enemy, and fled. The Germans achieved a complete breakthrough on a 80 km front between Namur and Sedan.

The German High Command then expected the panzers to pause while the infantry marched up to strengthen the crossings at the River Meuse. But Guderian shouted over the telephone to his superiors that he refused to delay and throw away the opportunity created by the breakthrough. He was allowed to advance for twenty-four hours, in which time his panzer corps of three divisions covered over 70 km. The German High Command was extremely worried about a flank attack from the south. Guderian was ordered to stop but objected strongly and was allowed to make a 'reconnaissance in force', which meant that he could not move his corps headquarters. He tricked his superiors by sweeping forwards another 80 km, communicating with his headquarters by landline telephone.

By 20 May Guderian could see the Channel and two days later reached Boulogne. The obvious allied action was an attack on the long flanks of the German thrust. The French General de Gaulle attacked from the south with only a few tanks but could not hold his gains without support from the rest of the army. Many in the French Command had been totally unprepared for the German attack, and its success had unnerved them so much that they were shocked into paralysis. Some British and French forces made a counter-attack at Arras: British Matilda tanks caught some of Rommel's motorised infantry, killed and wounded many. The German 37mm anti-tank guns, which were supposed to protect them, could not pierce the Matildas' armour. This shook Rommel, who hurried back to deal with the crisis. The advance of the Matildas was finally checked at the Battle of Arras.

The British fell back to the Canal line which Lord Gort, commander of the BEF, had strengthened. Surprisingly the Germans made a huge blunder when they did not use their panzers to take Dunkirk, the only port left from which the BEF could be evacuated. Hitler's motives for this are not known. Some historians have suggested that perhaps he wanted to keep his tanks for further fighting in France. Gort then carried out a planned series of withdrawals into a defensive area around Dunkirk. The Belgians' line cracked and they surrendered to the Germans.