John Lennon and Paul McCartney first met on July 6, 1957 at the St. Peter's Church Hall fête in Woolton. On that day, Lennon was performing with his band, The Quarrymen (sometimes written as The Quarry Men), for the church's annual garden festival. Although McCartney initially wasn't really interested in attending the gathering, he was convinced by his friend Ivan Vaughan that it might be a good place to meet girls. Paul had a change of mind.Vaughan, being a mutual friend of both 15 year old McCartney and 16 year old Lennon, introduced the aspiring musicians between the first and second of the Quarrymen's sets. Paul was also introduced to the other members of the group by Ivan, and he hung around for a while. At one point McCartney picked up a guitar and played one of Lennon's favorites, "Twenty Flight Rock", a song popularized by Eddie Cochran. Lennon was impressed with McCartney's singing the tune with the correct lyrics and proper chords. Paul then wrote down the lyrics of the song for John. Lennon himself had a short memory for lyrics as was evident when he sang the Del-Vikings' song "Come Go With Me" with incorrect and made up lyrics.
The Quarrymen would later include McCartney's friend, lead guitarist George Harrison, and other members would come and go. They would later evolve into The Beatles, a band you may have heard of before. But it all began at a certain church celebrating its annual garden festival, with that casual introduction of two teenagers who had the same passion for music. And the rest, as they say, is history. As a matter of fact, there's a whole book dedicated to the subject: The Day John Met Paul: An Hour-by-Hour Account of How the Beatles Began