Battle of Schöngrabern (or Hollabrunn)

Gazan's division, isolated in a gorge on the Danube, was encircled and attacked from all sides by a greatly superior Austro-Russian force. Mortier sent reinforcements to prevent annihilation. Fighting was bloody and intense, but the French managed to extricate themselves.

The Battle of Austerlitz, known as the "Battle of the Three Emperors," marks the apex of Napoleonic strategy. Facing a numerically superior allied army, Napoleon used ruse, meticulous preparation of the terrain, and the mobility of his troops to transform an apparently unfavorable position into a crushing victory. He deliberately placed his army on the Pratzen plateau, which he then had evacuated to lure the enemy into concentrating forces there. Convinced that the French right flank was weakened, the Austro-Russians committed the bulk of their troops to it. This maneuver dangerously weakened their center, which they believed out of reach. Napoleon waited until the enemy was fully committed to this error before ordering Soult's corps, concealed in the fog, to assault the plateau. The breakthrough at the center literally cut the allied army in two, sowing panic and making coordination impossible. On the wings, Davout and Lannes held or advanced according to plan, while Murat's cavalry and the Imperial Guard exploited the collapse of the enemy dispositions to capture thousands of prisoners. The rout was total: many Austro-Russian soldiers drowned attempting to flee across the frozen ponds of Satschan under French artillery fire. Austerlitz is not only a tactical masterpiece but also a political turning point for Europe; the victory placed Napoleon at the height of his glory and upended the continental balance.

The capitulation of Ulm ended the strategic encirclement orchestrated by Napoleon. Austrian General Karl Mack surrendered with nearly 27,000 men without a real battle, trapped by the Grande Armée's speed of maneuver.