Operation Cobra was an offensive launched by the First United States Army under Lieutenant General Omar Bradley seven weeks after the D-Day landings, during the Normandy campaign of World War II. The intention was to take advantage of the distraction of the Germans by the British and Canadian attacks around Caen in Operation Goodwood, and thereby break through the German defenses that were penning in their forces, while the Germans were unbalanced. Once a corridor had been created, the First Army would then be able to advance into Brittany, rolling up the German flanks once free of the constraints of the bocage country. After a slow start, the offensive gathered momentum and German resistance collapsed as scattered remnants of broken units fought to escape to the Seine. Lacking the resources to cope with the situation, the German response was ineffectual mainly due to the effect of Operation Bluecoat and the entire Normandy front soon collapsed. Operation Cobra, together with concurrent offensives by the British Second Army and the Canadian First Army, was decisive in securing an Allied victory in the Normandy campaign.

Having been delayed several times by poor weather, Operation Cobra commenced on 25 July 1944, with a concentrated aerial bombardment from thousands of Allied aircraft. The bombardments resulted in friendly fire casualties, including Lieutenant General Lesley J. McNair who was on the front line as an observer. Supporting offensives had drawn the bulk of German armored reserves toward the British and Canadian sector and, coupled with the general lack of men and materiel available to the Germans, it was impossible for them to form successive lines of defense. Units of the U.S. VII Corps led the initial two-division assault, while other First U.S. Army corps mounted supporting attacks designed to pin German units in place. Progress was slow on the first day but opposition started to crumble once the defensive crust had been broken. By 27 July, most organized resistance had been overcome and the VII and VIII Corps advanced rapidly, isolating the Cotentin Peninsula.

By 31 July, XIX Corps had destroyed the last forces opposing the First Army, which emerged from the bocage. Reinforcements were moved west by Field Marshal Günther von Kluge and employed in various counterattacks, the largest of which, Unternehmen Lüttich (Operation Liège), was launched on 7 August between Mortain and Avranches. Although this led to the bloodiest phase of the battle, it was mounted by already exhausted and understrength units and was a costly failure. On 8 August, troops of the newly activated Third United States Army captured the city of Le Mans, formerly the German 7th Army headquarters. Operation Cobra transformed the high-intensity infantry combat of Normandy into rapid maneuver warfare and led to the creation of the Falaise pocket and the loss of the German strategic position in northwestern France.

Following the successful Allied invasion of Normandy on 6 June 1944, progress inland was slow. To facilitate the Allied build-up in France and to secure room for further expansion, the deep water port of Cherbourg on the western flank of the U.S. sector and the historic town of Caen in the British and Canadian sector to the east, were early objectives. The original plan for the Normandy campaign envisioned strong offensive efforts in both sectors, in which the Second Army (Lieutenant-General Sir Miles Dempsey) would secure Caen and the area south of it and the First U.S. Army (Lieutenant General Omar Bradley) would "wheel round" to the Loire valley.

General Sir Bernard Montgomery—commanding all Allied ground forces in Normandy—intended Caen to be taken on D-Day, while Cherbourg was expected to fall 15 days later. The Second Army was to seize Caen and then form a front to the southeast, extending to Caumont-l'Éventé, to acquire airfields and protect the left flank of the First U.S. Army as it moved on Cherbourg. Possession of Caen and its surroundings—desirable for open terrain that would permit maneuver warfare—would also give the Second Army a suitable staging area for a push south to capture Falaise, which could be used as the pivot for a swing east to advance on Argentan and then the Touques River. The capture of Caen has been described by the British official historian Lionel Ellis as the most important D-Day objective assigned to the British I Corps (Lieutenant-General John Crocker). Ellis and Chester Wilmot called the Allied plan "ambitious" since the Caen sector contained the strongest defenses in Normandy.

The initial attempt by I Corps to reach the city on D-Day was blocked by elements of the 21st Panzer Division and with the Germans committing most of the reinforcements sent to meet the invasion to the defense of Caen, the Anglo-Canadian front rapidly congealed short of the Second Army's objectives. Operation Perch in the week following D-Day and Operation Epsom (26–30 June) brought some territorial gains and depleted its defenders but Caen remained in German hands until Operation Charnwood (7–9 July), when the Second Army managed to take the northern part of the city up to the River Orne in a frontal assault.

The successive Anglo-Canadian offensives around Caen kept the best of the German forces in Normandy, including most of the armor, to the eastern end of the Allied lodgement but even so the First U.S. Army made slow progress against dogged German resistance. In part, operations were slow due to the constraints of the bocage landscape of densely packed banked hedgerows, sunken lanes and small woods, for which U.S. units had not trained. With no ports in Allied hands, all reinforcement and supply had to take place over the beaches via the two Mulberry harbors and were at the mercy of the weather.

On 19 June, a severe storm descended on the English Channel, lasting for three days and causing significant delays to the Allied build-up and the cancellation of some operations. The First U.S. Army advance in the western sector was eventually halted by Bradley before the town of Saint-Lô, to concentrate on the seizure of Cherbourg. The defense of Cherbourg consisted largely of four German battlegroups formed from the remnants of units that had retreated up the Cotentin Peninsula, but the port defenses had been designed principally to meet an attack from the sea. Organized German resistance finally ended on 27 June, when the U.S. 9th Infantry Division managed to reduce the defenses of Cap de la Hague, north-west of the port. Within four days, VII Corps (Major General J. Lawton Collins) resumed the offensive toward Saint-Lô, alongside XIX Corps and VIII Corps, causing the Germans to move more armor into the U.S. sector.