"Love Me Do" is the Beatles' first single, backed by "P.S. I Love You". When the single was originally released in the United Kingdom on 5 October 1962, it peaked at No. 17; in 1982 it was re-promoted (not re-issued, retaining the same catalogue number) and reached No. 4. In the United States the single was a No. 1 hit in 1964. In 2013, recordings of the song that were published in 1962 entered the public domain in Europe.

The song was written several years before it was recorded, and prior to the existence of the group named the Beatles. The single features John Lennon's prominent harmonica playing and duet vocals by him and Paul McCartney. Three different recorded versions of the song by the Beatles have been released, each with a different drummer.

Love Me Do was primarily written by Paul McCartney in 1958–1959 while playing truant from school at age 16 and later credited to Lennon–McCartney; John Lennon contributed the middle eight. Lennon: "Paul wrote the main structure of this when he was 16, or even earlier. I think I had something to do with the middle ... 'Love Me Do' is Paul's song. He wrote it when he was a teenager. Let me think. I might have helped on the middle eight, but I couldn't swear to it. I do know he had the song around, in Hamburg, even, way, way before we were songwriters". (David Sheff. John Lennon: All We Are Saying). McCartney: "'Love Me Do' was completely co-written. It might have been my original idea but some of them really were 50-50s, and I think that one was. It was just Lennon and McCartney sitting down without either of us having a particularly original idea. We loved doing it, it was a very interesting thing to try and learn to do, to become songwriters. I think why we eventually got so strong was we wrote so much through our formative period. 'Love Me Do' was our first hit, which ironically is one of the two songs that we control, because when we first signed to EMI they had a publishing company called Ardmore and Beechwood which took the two songs, 'Love Me Do' and 'P.S. I Love You', and in doing a deal somewhere along the way we were able to get them back".

...
Wikipedia