UW-Extension's website includes a general history and a timeline. See http://www.uwex.edu/about/uw-extension-history.html
Research in the archival records: read the finding aid at http://digital.library.wisc.edu/1711.dl/wiarchives.uw-mil-uwmac0071 and ask in the Archives.
The Extension existed under various names in Milwaukee from 1892 to present day. It is now Milwaukee County Cooperative Extension.
University of Wisconsin - Milwaukee (UWM) was established in 1956 after the merger of Wisconsin State College, Milwaukee with the Milwaukee Extension Division of the University of Wisconsin.
1891 - University of Wisconsin, located in Madison, WI started the University Extension, which offered correspondence courses and lecture courses
1892 - University Extension offered classes in Milwaukee in the old Empire building located at Grand Avenue and West Water Streets (now Wisconsin and Plankington Avenues)
1892 - 1920 - School officially known as University of Wisconsin College and Vocational Day and Evening Classes in Milwaukee
1910 - School moved to 471 Van Buren Street
1920 - 1930 - School changes its name to The University of Wisconsin Extension Division
1922 - 1956 Students informally refer to the school as The Division
1924 - School moved to 137 Second Street (now 637 Second Street)
1928 - School moved to Milwaukee Center building at Sixth and State Streets
1941 - First university extension graduate courses leading to advanced degrees offered
1945 - Became official division school of the University of Wisconsin
1946 - Classes were being held in eight locations due to shortage of space: West Allis, South Milwaukee, Wauwatosa, Shorewood and the Metropolitan Building, Brumber Building and Wisconsin Tower in Milwaukee.
1953 - New building, facing Kilbourn Avenue, opened
1955 - Legislature passed measure combining Wisconsin State College, Milwaukee and the Milwaukee Extension Division. UW-Milwaukee formed in 1956.