Sorry for the long update, but I've finished up the rest of the war in Europe.
Operation Roundup and the Liberation of Europe (May-December 1943)
After the successes in the Mediterranean theater, the Americans again pushed for an invasion of mainland Europe; they were supported by the French, who were eager to free their homeland. Although the British were skeptical of the plans, they were convinced to participate in the invasion, code named Operation Roundup. Set for late May of 1943, Roundup consisted of British, American, French, and Commonwealth troops landing on six beaches : Utah, Omaha, Gold, Juno, Sword, and Cutlass. The Americans would land on Utah and Omaha, the British at Gold and Sword, the Commonwealth at Juno, and the French and other Allies at Cutlass. Preparations continued for months, including a deception ploy that convinced the Germans the invasion would come in the Pas de Calais in July.
On the morning of May 29, 1943, the invasion flotilla sailed hard and fast across the English Channel. The initial landings went off smoothly, as most of the planned defenses for the Atlantic Wall had not yet been placed by the Germans. The Allies quickly made headway, easily achieving and surpassing their goal lines for the day. The heaviest fighting took place around Omaha and Cutlass beaches; Omaha came up against a small group of Panzers, which were destroyed only with the arrival of American M4 tanks. Meanwhile Cutlass abutted the garrison town of Le Havre, and the French, Belgian, and Dutch troops had to wade through urban warfare for several days before pushing the Germans out of the city.
The Allies continued to swiftly advance into Normandy, entering Cherbourg on June 13th and Avranches on July 5th. The fighting grew heavier near Paris and Brest, but Brittany was fully liberated by late August and Paris was captured on August 1st. The Allies soon ran into significant resistance, near Orleans and Reims; these massive battles checked the Allied advance for almost a month in September, but the Germans broke under the continued onslaught and the Allies advance resumed. The Rhine was reached in late December; now the end of the war was in sight, and the Allies were poised to deliver the final blow to Nazi Germany.
Felling Hitler's Reich (January-August 1944)
The final phase of the European war was characterized in the West by two major operations: Operation Ruby, the invasion of the Balkans through Albania, and Operation Overlord, the invasion of Germany proper. Both were large undertakings against a reeling foe, and in the end both devolved into races for land against the Soviets.
Operation Ruby was an almost purely British operation; the French had little manpower to spare, and the Americans had no interest in opening up another front in Europe. Thus, Prime Minister Churchill's proposal was commanded by Bernard Montgomery, a British General, and was carried out almost exclusively by British and Commonwealth troops. The Americans did not leave the British out to dry, however; they supplied most of the air cover in P-51 Mustangs, and the first P-59 Airacomets. They also contributed a mechanized division to the advance into Yugoslavia. The British, however, had significant interest in the region, and desired to minimize postwar Soviet influence in the area. They also were committed to fulfilling an obligation to the Greeks in 1941, after the German invasion of the Balkans
Thus, on March 17th 1944, the British stormed a lonely beach in central Albania, much to the surprise of the Italian and German troops stationed there. The nearby town of Durres was taken in just a few hours, as the Balkans had been almost drained of Axis manpower for fighting the approaching Soviets. The British concentrated on capturing the Albanian capital of Tirana, while Canadian forces moved southwards to Vlore; meanwhile Australians and New Zealanders concentrated on holding the northern flank. Tirana was liberated on March 24th, with a fair amount of street fighting. On the 27th the British began advancing eastwards into Macedonia; to the south, the Canadians were just crossing the Greek border.
Meanwhile the American 3rd Mechanized Division offloaded at Durres and began moving northeast. Further reinforcements would soon arrive for the Allies, most of them bound for Greece after landing. However, the current objective was the Bulgarian capitol of Sofia, in order to force a surrender. The Bulgarians put up a ferocious defense, with a fighting retreat across Macedonia, costing the British heavy casualties as they advanced into Skopje. The Canadians, now joined by the Americans, advanced on Ioannina, capturing it on April 21st. To the north, the Australians had reached Podgorica and had halted to consolidate their supply lines.
During this time the Yugoslav countryside had erupted into a multi-sided war. Tito's communist partisans rose up in Serbia and eastern Croatia; the Chetniks rose up in central Serbia and eastern Bosnia; the Croatian Ustase began slaughtering Bosniaks, while the Slovenes rose up against the Germans.
It was into this quagmire that the Allied armies in Italy began marching in late April; General Mark Clark moved his army into Slovenia and Istria, taking a fair amount of casualties in the difficult terrain. In the south the British continued to push across Macedonia into Bulgaria; Sofia was surrounded on May 12th and was under siege into early June. Pristina, in Yugoslavia, fell to the Allies on May 29th, while Thessaloniki was liberated on June 1st. Athens finally fell on July 3rd to General Crerar's forces. Turkey also entered the war for the Allies, occupying parts of southeastern Bulgaria. When the war finally ended, the Allies had advance to within 80 miles of Belgrade, and General Clark's army had just captured Zagreb.
The war in northern Europe had continued unabated over the winter months, with the Allies unwilling to cross the freezing Rhine for several weeks. Instead they concentrated on liberating the Low Countries, with Brussels being the first capital to fall in October of 1943. In a rather ironic twist, one of the Allied offensives pushed through the Ardennes forest in a near reversal of the German attack in 1940. This offensive pushed the Germans out of eastern Belgium and Luxembourg, only leaving a salient around the Flemish town of Antwerp. Antwerp was taken by General Patton's 3rd Army in early January, and the Allies began pushing into the Netherlands. By the end of January, both Maastricht and Rotterdam had been liberated, and the Allied focus shifted back towards Germany.
Karlsruhe was the first major city to fall, on February 4th; next was Dusseldorf, on the 9th. The Germans, despite fighting on their home territory, were unable to offer more than a meager resistance, and many soldiers simply surrendered than continue a hopeless fight. Frankfurt fell on March 1st, Bremen on the 20th. The Allied advance continued further, reaching Nuremburg in early April.
By early July, the Allies had reached the outskirts of Berlin, entering the city on July 8th. Hitler reluctantly agreed to evacuate east towards the still German city of Danzig to flee to neutral Sweden. However, his car was intercepted and captured outside the city by a pair of American tanks; afterwards, Heinrich Himmler declared himself Fuhrer and moved the Reich's base of operations to Danzig. Despite Himmler's optimism, most Germans had accepted defeat when on August 5th, General Omar Bradley's 5th Army entered Poland. That same day, Heinrich Himmler was arrested by the German high command, and temporary Fuhrer Erich von Manstein requested a ceasefire with the Allies. Over the next 36 hours, the few German troops still fighting laid down their arms. The war in Europe was over.