The first Madison Square Garden was constructed in 1871
Barnum's Monster Classical and Geological Hippodrome
and Madison Avenue
(4th avenue). Architect Stanford White
bought this open-air venue of fire eaters and chariot races and changed
its name to "Madison Square Garden" in 1879.
The second Madison Square Garden was designed by White and built on
the site of the first in 1889. In 1906, White was shot dead in
the Garden's rooftop cabaret by a man he had allegedly cuckolded.
The New York Life Company owned the land it was on, and in 1925 they
decided the land was a good place for their headquarters.
The third Madison Square Garden was built in 1925 on Eighth Avenue
between 49th and 50th Streets. The building was eventually
torn down, and is now the site of World Wide Plaza.
The fourth Madison Square Garden (the current one) was built between
1963 and 1968 on top of a new Pennsylvania Station on Seventh Avenue
between 31st and 33rd Streets.
Pieced together from
plus a tidbit or two from perdedor.