History
Updated
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The first two stood on the square itself, the third moved to Eighth Avenue and the fourth, opened in 1968, sits on top of Penn Station.

The name Madison Square Garden has stayed fixed since 1879, but the building has not. Four arenas have carried the name, and only the first two were actually at Madison Square.
The first Garden: 1879
The first Madison Square Garden was a converted railroad depot at East 26th Street and Madison Avenue, which had been used by P. T. Barnum as a hippodrome. It was renamed Madison Square Garden in 1879 and was used for circuses, sporting events and public shows.
The second Garden: 1890
A new, larger building was opened in 1890 on the same site, designed by the architect Stanford White. It was a tall, ornamented structure with a tower, and it held the city's largest arena until it was demolished in 1925.
The third Garden: 1925
The third Garden opened in 1925 on Eighth Avenue between 49th and 50th Streets. It was the first of the arenas that was not on Madison Square, and it was home to the Rangers, who joined the NHL in 1926, and later to the Knicks, who started in 1946.
The fourth Garden: 1968
The current arena opened in February 1968 on top of Pennsylvania Station, on Seventh Avenue between 31st and 33rd Streets. It was the site of the first fight between Muhammad Ali and Joe Frazier on March 8, 1971, known as the Fight of the Century.
Rebuilt without closing
The arena was renovated in stages between 2011 and 2013, with work done in summer off-seasons so that the building could remain open. The renovation replaced the seating and concourses and added suites. The roof and the structure were left as they were, which is why the Garden is described as both the oldest and the newest of the region's arenas.