"In 1889, Almon Strowger, of Kansas City, Missouri, was inspired by the idea of manufacturing automatic telephone exchanges that would not require switchboard operators. He founded the Strowger Automatic Telephone Exchange Company in 1891, which held the first patents for the automatic telephone exchange. Subsequently, in 1901, Strowger helped form the Automatic Electric Company to which he leased his patents exclusively" . (From Wikipedia)
One the diagram below we see :
One "Line finder" switch. Two "Selector" Switches. One "Connector" Switch
The Strowger switch
Almon B. Strowger developed a system of automatic switching using an electromechanicalcal switch based around around electromagnets and pawls. In 1888 he took out a US Patent No. 447918 10/6/1891.
Automatic switching was first invented by Connolly & McTigthe in 1879, but strowger first used it.
In October 1891 the 'Strowger Automatic Telephone Exchange' was started.
The theory of the selector.
The selecetor start in the "Home" position and will move to the selected telephone depending on the number of "Pulses" send to the relay arm.