Like is so often true, the answer depends upon your point of view. If looking for the first documented device that could do the job the answer is Archimedes, but . . .
Archimedes invented a vertical box moved up and down by a set of ropes and pulleys with the power source to move the ropes being horses or men pulling on the ropes. Primitive elevators of this kind can be documented to have been used throughout the Middle Ages to move cargo or other heavy loads vertically. The first elevator specifically designed to move people was installed at Versailles for Louis XIV. The King could enter a lift chair from an outside balcony, and men inside the walls could use ropes and pulleys attached to counterweights to lift or lower his royal personage, but the first device truly resembling what we now call an elevator and designed to carry passengers was built by Elisha Graves Otis.
Like in so many other cases, the steam engine revolutionized what was possible for moving heavy loads vertically, and hydraulics was not far behind. Still, by 1850 this sort of lifting was still considered dangerous and usually limited to heavy engineering and construction applications. Elisha Graves Otis changed all of that, and made the kind of machine most people usually think of when hearing the word “elevator” possible by inventing a safety brake in 1852 for freight elevators. Elevators with this brake were so safe that riding in them did not seem like the least bit of risk. The cable could completely break and the elevator would not fall. It didn’t take long for Otis to realize the potential of his elevators for carrying passengers to the upper floors of tall buildings. He displayed his machines at the World’s Fair in the Crystal Palace in New York. He installed his first passenger elevator in a New York Department store in 1857, and by 1873 there were over 2000 Otis elevators in operation.
Elisha Otis continued in the business and design of elevators throughout the rest of his life. When he died in 1861 his sons Charles and Norton followed in his footsteps with the family registering patents for improvements in elevator design in 1861 and 1903. When his sons took over the company they changed the name to Otis Brothers & Company which later merged with a number of other elevator manufacturers to form the Otis Elevator Company. This American inventor from Vermont is, without a doubt, the father of the modern passenger elevators that make high rise buildings, metropolitan skylines, and city life what they are today.