The School of Dentistry occupies connected buildings from different eras, and the oldest part is the Kellogg Building. It’s full name is the W. K. Kellogg Foundation Institute: Graduate and Postgraduate Dentistry. The building was dedicated in 1940, and it was paid for with a mix of funds from the Kellogg Foundation and from the federal Works Progress Administration. The building's entrance on Fletcher Street still looks pretty similar to the picture postcard from eighty years ago!
The postcard is from the Bentley Historical Library's digital collections. Their website, https://bentley.umich.edu/ is a great place to search for state of Michigan and University of Michigan topics.