Who inveted the drum kit?

It's nigh impossible to say who invented the drum kit because it's evolved over more than a century.

Back in the late 1800's bands mostly had one person for each of the bass drum, snare drum, cymbal etc. When vaudeville got into its stride around 1900 and musicians played in the pit, there wasn't enough space for a bunch of percussionists, so they looked at playing more than one thing at a time. There was a patent for a bass drum pedal in 1888 which meant one person could play two things at the same time. By 1910 the Ludwig brothers had made a pedal with a spring and eventually one that could change from cymbal to bass drum using a switch. In 1918 Ludwig were marketing a drum kit which might have been the first commercial one. The kit evolved over time to what it is now, mostly because musicians are known for being inventive and changing things to suit themselves. So in one way you might say Ludwig but in truth it was a multitude of drummers who contributed to the existence of a drum kit.