This was written by John Lennon and credited as always to Lennon-McCartney. It was the group’s s second single (after Love Me Do) and their first No 1. (Wikipedia says: ‘The single was released in the UK on 11 January 1963 and reached No 1 on the New Musical Express and Melody Maker charts. However, it only reached No 2 on the Record Retailer chart, which subsequently evolved into the UK Singles Chart. Because of this, it was not included on the Beatles’ number ones compilation.’ No one around at the time took any notice of Record Retailer, so in my book it was their first No 1.) It was released in the US in February 1963 and did nothing, but on re-release in January 1964 it went to No 3.
Here is a live performance from 1964.