SMS Lützow was a German Kaiserliche Marine battlecruiser under Capt. Harder, flagship of Vice Admiral Franz von Hipper's Scouting Group I battlecruiser fleet in World War I.

She was commissioned in 1915, displacing ~27,000 tons with a main armament of 8 x 12 in (305 mm) guns, making her the largest and most powerful German battlecruiser to date along with her elder sister Derfflinger.

She led Scouting Group I at the Battle of Jutland on 31 May 1916. In this engagement her accurate fire in the early battlecruiser action (begining at 15:48) knocked out the Q turret (13.5" (343 mm)) of HMS Lion, the lead Royal Navy battlecruiser, starting a catastrophic fire that, but for the quick-witted heroism of the turret's mortally injured commanding officer, would have subjected Lion to the same lethal magazine explosion that befell 3 other British battlecruisers that day. Lützow proceeded to take heavy punishment from her British counterparts as the main battle was joined in early evening on 31 May, though her own fire remained deadly: British armored cruiser HMS Defence, rushing to finish off the foundering light cruiser SMS Wiesbaden between the opposing fleets, was hammered by Lützow and other leading German capital ships, disintegrating spectacularly at 18:20.

At about this moment, however, Lützow and Derfflinger came within range of a fresh squadron of British battlecruisers led by Rear-Admiral Hood in HMS Invincible - the original design of all battlecruisers. Two 12" (305 mm) shells from Invincible penetrated Lützow below the water line leading to severe flooding. However at about 18:30 - the very moment the Grand Fleet first "crossed the T" of the High Seas Fleet - Invincible suddenly appeared before Lützow and Derfflinger as a perfect target steaming 5 miles (8 km) away. Several 12" (305 mm) salvos later, Invincible blew up and sank with all but 6 of her 1,032 crew, Admiral Hood included. Lützow steadily fell behind the main fleet as flooding worsened, forcing Hipper to transfer his flag to a destroyer around 19:00.

In the following hour Lützow continued to sustain damage, taking a total of 24 heavy-calibre shells from 12", 13.5" and 15" guns. The 2 12" (305 mm) hits below the waterline from Invincible were the most serious. In the night action of 31st May/1st June Lützow was abandoned by her 1,150 surviving and scuttled, her escape from the battle area being reckoned hopeless. She was the biggest German ship sunk by British gunfire in the war.