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.
Art Is... was created in 1971.
This Is Not Art was created in 1998.
The Art of Making Art was created on 2011-10-23.
The Art of The Trio was created in 1980.
Art of Motion was created in 2005.
ART Teenz was created in 1998.
The Art of Discworld was created in 2004.
Art of Cookery was created in 1747.
The Art of Happiness was created in 1998.
Art Bleeds was created in 1999.
The art of the faker was created in 1959.