Being a modern city there isn't even any history
Cobblers. It has a rich a history as any city in the UK, more than most in fact.
Birmingham was the first industrialised city in England. The early 19th century saw the formation of the 'Lunar Society of Birmingham' where eminent scientists, writers and philosophers met to discuss the development of modern society. Where Watt and Boulton developed the first practical steam engines. (You can visit SoHO house where it all happened)
This history is written large across the grandiose town hall, council chambers and the livid red brick Victorian buildings that weren't demolished by the Luftwaffe or misguided town planners in the 1960s. You can also see the human cost of rapid industrialisation by visiting the Back to Back houses run by the national trust.
In the 20th century it became the hub of the UK car manufacturing industry which made it a target for the Luftwaffe and after the war became home to people from across the Commonwealth and beyond, who all shaped city life with new clothes, customs and food, hence the amazing Balti Belt.
The history of industrial revolution, empire, decline and post colonisation is inscribed on the very fabric of the city, free for anyone with a set of eyes and a bit of curiosity.
It also has a fantastic City Art Gallery and the oldest operated cinema in England (The Electric, which is an ace Arts cinema).