Short answers, pulled from the story.
The Battle of Kiev resulted in 452,700 Soviet soldiers being trapped in the encirclement, of whom only 15,000 escaped by the 2nd of October 1941. Total Southwestern Front casualties reached 700,544, including 616,304 killed, captured, or missing.
The Battle of Kiev is recorded as the largest encirclement in the history of warfare by number of troops. Five Soviet armies totaling 452,700 soldiers, along with 2,642 guns and mortars and 64 tanks, were trapped in a pocket covering approximately 20,000 square kilometers southeast of Kiev.
The Soviet Southwestern Front was effectively destroyed. Its five armies, the 5th, 21st, 26th, 37th, and 38th, comprising 43 divisions, were almost annihilated. The Front suffered 700,544 total casualties and had to be rebuilt nearly from scratch, as the Western Front had been before it.
Stalin repeatedly refused to authorize a withdrawal despite clear warnings from his commanders. When General Zhukov recommended pulling back behind the Dnieper River in late July 1941, Stalin dismissed him as chief of staff. In September, Stalin also rejected Marshal Budyonny's request to retreat 250 kilometers to the Psyol River, forbade destruction of the bridges, and ordered Kiev held at all costs.
Mikhail Kirponos was the commander of the Soviet Southwestern Front at Kiev. Trapped inside the German encirclement after the ring closed on the 16th of September 1941, he was killed while attempting to break out through German lines.
Guderian's Panzer Group 2 pivoted south from Army Group Center on Hitler's order of the 21st of August 1941. After capturing the intact 800-meter Desna River bridge at Novgorod-Seversky on the 26th of August, the group drove through Soviet lines, capturing Gomel on the 21st of August and reaching the Kiev region by mid-September to link up with Panzer Group 1 south of Lokhvytsia on the 16th of September.