The origins...
Badminton as it is played today was probably invented by British army officers in India in the 19th century, which is also when it was first played competitively. In a possible early Chinese predecessor, players would try and use their hands to keep a shuttlecock (of a different kind than the one used for badminton today) in the air for as long as possible.
...and the development of today's game
Slightly closer to today's sport is a popular children's game played from Medieval to Victorian times in England. "Battledore and Shuttles" involved using paddles to hit a shuttle. The aim of the game was to keep the shuttle in the air for as long as possible. However, "Battledore and Shuttles" was played outside on the street, getting in the way of those who wanted to use streets to get from A to B, and not to amuse themselves...
Notwithstanding this rather common predecessor, the game appealed to the English nobility, too, and in the 19th century, British Army officers in India invented a game similar to today's badminton. This was also when a net was used for the first time. The game, at that time still called Poona (after the city where it was invented), was brought back to England by returning soldiers in the 1850s. There, the Duke of Beaufort was so taken in by the sport that it became a regular form of entertainment at his estate in Gloucestershire: Badminton House. From there, the game, which was soon to take the name of the manor where it first became sociable in England, spread throughout the country.
The first official set of rules was written by the Bath Badminton Club as early as 1877. In 1893 the Badminton Association of England was established and in 1899, the first official international championship took place: the All England Badminton Championships. More than a century later, the "All England" is still regarded as one of the most prestigious badminton competitions in the world.
In 1934, the International Badminton Federation was set up in the UK and became badminton's first international governing body. Founding member countries were England, Ireland, Scotland, Wales, Denmark, Holland, Canada, New Zealand and France, India joined in 1936. Today, the International Badminton Federation has grown to 153 member countries, including 48 European countries, and is based in Kuala Lumpur.