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The 18th century philosopher David Hume (1711-1776) is considered one of the most important figures in the history of Western philosophy and the Scottish Enlightenment. He is buried in the Old Calton Hill cemetery, seen in the lower part of the picture above. This view is looking from the Calton Hill towards the Old Town. His tomb is the rotunda, of which more below. 

The tomb is by Robert Adam, 1777. ... a grandly Roman cylinder of rough ashlar with a fluted frieze on the lower stage, a bold Doric entablature on the upper. Big urn in a niche above the doorpiece. Adam's preliminary sketches show that the tomb of Theodoric at Ravenna was the starting point for his design. (From Edinburgh by John Gifford, Colin McWilliam and David Walker (1991), Yale University Press).  More by Robert Adam in Edinburgh.

There is a modern statue of 1997 to David Hume in the High Street (Royal Mile). More about the statue.