Short answers, pulled from the story.
Paul McCartney joined the Quarrymen in August 1957 after performing the instrumental song Raunchy on the upper deck of a bus. John Lennon recruited McCartney despite initial hesitation about George Harrison's age. The group later evolved through names like the Silver Beetles before settling on the Beatles in August 1960.
The Beatles arrived at John F. Kennedy International Airport to a crowd of 3,000 screaming fans on the 7th of February 1964. Their first live US television performance on The Ed Sullivan Show was watched by approximately 73 million viewers. This event ignited Beatlemania and marked the beginning of the British Invasion in America.
The Beatles performed their last commercial concert at San Francisco's Candlestick Park on the 29th of August 1966. They stopped touring because their music could no longer be heard over the screams of their fans. This decision allowed the band to embrace an increasingly experimental approach in the studio.
Tensions during the recording of the White Album from late May to mid-October 1968 were caused by openly divisive relations between the members. Ringo Starr quit for two weeks and John Lennon lost interest in collaborating with Paul McCartney. Lennon also insisted on bringing Yoko Ono to the sessions despite the rule that girlfriends were not allowed in the studio.
The Beatles performed their final live show on the rooftop of the Apple Corps building at 3 Savile Row on the 30th of January 1969. The Get Back sessions were a miserable recording experience that led George Harrison to walk out for five days. The project eventually resulted in the Abbey Road album which topped the UK charts for seventeen weeks.
Paul McCartney publicly announced his departure from the band on the 10th of April 1970. The Beatles' contractual partnership was not formalized until the 29th of December 1974 when John Lennon signed the paperwork terminating the partnership. The band holds the record for most number-one albums on the UK Albums Chart with 15 entries.