Short answers, pulled from the story.
The Battle of Taiyuan was fought in 1937 as part of the Second Sino-Japanese War. The final assault on the city itself occurred in early November, with Taiyuan falling by the night of the 9th of November 1937.
Chinese forces were commanded by Yan Xishan, the warlord of Shanxi; Wei Lihuang of the 14th Army Group; and Fu Zuoyi of the 7th Army Group. Zhu De led the Eighth Route Army of the Chinese Communist Party, which participated under the Second United Front alliance.
The Japanese Northern China Area Army was under Hisaichi Terauchi. The operation also involved elements of the Kwantung Army and the Inner Mongolian Army led by Demchugdongrub. Lieutenant General Itagaki commanded the 5th Division, a key formation in the battle.
Japan won a decisive victory, capturing Taiyuan and most of Shanxi Province. The battle effectively ended large-scale organized Chinese resistance in the North China area. China lost 20,000 men and 80 artillery pieces in the defense of the city, with tens of thousands of civilians also killed or injured.
On the 25th of September 1937, Lin Biao's 115th Division ambushed Japanese supply columns of the 5th Division between Xiaohan Village and Guankou Village, inflicting between 150 and 240 casualties. The 5th Division ultimately suffered 1,070 casualties in the Pingxing Pass operation, and combined Japanese losses there reached 1,506.
Taiyuan was the capital of Shanxi Province and housed the National Revolutionary Army's arsenal. Its capture gave Japan access to coal from Datong in northern Shanxi. However, holding the territory also tied down significant Japanese forces because of ongoing guerrilla attacks by Nationalist and Communist units.