Who invented the cinema?

No one person invented cinema. However, in 1891 the Edison Company successfully demonstrated a prototype of the Kinetoscope, which enabled one person at a time to view moving pictures.

The first public Kinetoscope demonstration took place in 1893. By 1894 the Kinetoscope was a commercial success, with public parlours established around the world.

The first to present projected moving pictures to a paying audience were the Lumière brothers in December 1895 in Paris, France. They used a device of their own making, the Cinématographe, which was a camera, a projector and a film printer all in one.

There was no specific moment when the cinema was invented and no individual inventor. The cinema is the modern version of what used to be called a 'camera obscura' from before photographic film was invented. A camera obscura was darkened room or booth with a small opening to the outside world. Light coming through the small opening hit one of the walls and created a moving image of the world outside. Sometimes lenses and mirrors were used to capture the light and focus it on the wall. People had never seen anything like it and thought it magical.  When film and projectors were invented, it became possible to have bigger rooms and to show images other than the world outside the building. The buildings were given different names but we know them as cinemas.

Small versions of the camera obscura were used by artists to project an image onto their canvas so they could sketch its outline and get all the proportions right before painting it.

The first moving picture was made in 1887 by Eadweard Maybridge.  It consisted of several shots of a horse running that where shown in sequence.   It is the first stop motion animation. The footage proved that  a running horse at regular intervals had all four hooves in the air. 

Commercial showing of films didn't become popular till after 1900.