The Art of the Start was created in 2004.
Sorry, but the term "contemporary" art isn't a movement in art. That means contemporary art of the 1920s is art that was in the process of being created during the 1920s, and contemporary art of today is art that is being created today. To answer your question literally, contemporary art starts now. But I think you may mean when did the idea of modern art come into play. I would say the 1950s are the start of what we call modern art and that it turned into modern art in roughly the 1970s.
This Is Not Art was created in 1998.
Art Is... was created in 1971.
The Art of Making Art was created on 2011-10-23.
Unique Art was created in 1916.
Art Contest was created in 2003.
Art from the Heart was created in 1985.
The Art of Cricket was created in 1958.
Art of Noise was created in 1983.
Art Chicago was created in 1980.
The Art of The Trio was created in 1980.
The Art of Seeing was created in 1942.