Neil Armstrong died last Saturday aged 82.
The funeral in Cincinnati, Ohio, was by invitation only, reflecting Neil Armstrong’s own intensely private nature.
Hundreds of millions watched Neil Armstrong land on the Moon on 20 July 1969 and describe it as: “One small step for a man, one giant leap for mankind.”
The line became one of the most famous quotes of the 20th Century.
On Friday, Neil Armstrong’s family and friends as well as fellow astronauts gathered at a private golf club for the funeral.
“Neil Armstrong’s first step on the Moon paved the way for others to be the <<first>> to step foot on another planet,” said Charles Bolden, head of the US space agency Nasa.
Flags flew half-mast across America on Friday, following President Barack Obama’s order to mark the funeral.
The president earlier described Neil Armstrong as “a hero not just of his time, but of all time”.
A public memorial for the astronaut is planned on 12 September in Washington.
Neil Armstrong’s family said last Saturday that he had died from complications after heart surgery.
The family statement praised him as a “reluctant American hero” and urged his fans to honor his example of “service, accomplishment and modesty”.
Last November, Neil Armstrong received the Congressional Gold Medal – the highest US civilian award.
Many of his colleagues and friends have paid tribute to him as a modest man who never sought the limelight.
Michael Collins, a pilot on the Apollo 11 Moon mission, said: “He was the best, and I will miss him terribly.”
In a rare interview with Australian TV this year, he reflected on a moment during his three hours on the Moon when he stopped to commemorate US astronauts and Soviet cosmonauts who had died in action.
Neil Armstrong and fellow astronaut Edwin “Buzz” Aldrin collected samples, conducted experiments and took photographs during their moonwalk.
Apollo 11 was Neil Armstrong’s last space mission. In 1971, he left NASA to teach aerospace engineering.
Born in 1930 and raised in Ohio, Neil Armstrong took his first flight aged six with his father and formed a lifelong passion for flying.
Neil Armstrong flew Navy fighter jets during the Korean War in the 1950s, and joined the US space programme in 1962.
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