The Scottish inventor, Alexander Bain, received British patent 9745 on May 27th, 1843 for his "Electric Printing Telegraph". Frederick Bakewell made several improvements on Bain's design and then the Pantelegraph was invented by Italian physicist Giovanni Caselli. He introduced the first commercial telefax service between Paris and Lyon in 1865, some 11 years before the invention of the telephone.

Fax machines have evolved, especially after wireless transmissions became available to the home user. The Xerox Corporation was an early contributor to the process as was Lockheed.

More Info: en.wikipedia.org