The Moon's physical exploration started when on September 14, 1959, Luna 2, a space probe launched by the Soviet Union, impacted the Moon's surface, becoming the first man made structure to land on moon. Before that, Earth observation was the only accessible means of exploration. The optical telescope invention led to the first leap in lunar observation quality.
Galileo Galilei is usually credited as the first individual to use a telescope for astronomical purposes; having produced his own telescope in 1609. It was among his first observations that the mountains and craters on the lunar surface were discovered.
Here is a brief history of lunar exploration :