Short answers, pulled from the story.
The Battle of Vitebsk took place on the 26th and the 27th of July 1812, during the French invasion of Russia. It was part of Napoleon's broader campaign to envelop and destroy the Russian First Army before it could escape.
General Pyotr Konovnitsyn led the Russian rearguard on the 26th of July, and General Peter Graf von der Pahlen commanded the delaying force on the 27th. Overall command of the Russian First Army belonged to General Michael Andreas Barclay de Tolly.
Barclay changed his plan after receiving news that Bagration's Second Army had been defeated at the Battle of Saltanovka by Marshal Louis Nicolas Davout, making a linkup impossible. With Napoleon capable of cutting between the two Russian armies and reaching Smolensk first, Barclay's advisers persuaded him late on the 26th of July to order a retreat rather than risk the First Army in a stand.
The Russian main force began moving out at around 16:00 on the 27th of July while a rearguard under General Pahlen kept the French occupied. Cossack parties stayed behind and kept camp fires burning through the night, deceiving Napoleon into believing the army had remained in position. He discovered the battlefield was empty only the next morning.
French casualty estimates were disputed: historian Riehn put them at 400 killed, 900 wounded, and 70 captured, while Bodart estimated 3,400 killed and wounded with 300 captured. Russian losses amounted to roughly 3,000 men killed and wounded. Among the French dead was Colonel Liedat, commander of the general staff of the army's military engineer corps.
The Russian First Army conducted an orderly retreat to Smolensk, where it successfully united with Bagration's Second Army, exactly as Barclay de Tolly had planned. That union set the stage for the Battle of Smolensk, a far larger engagement that followed shortly afterward.