“Martha My Dear” is a piano-driven track named after Paul McCartney’s sheepdog, Martha. McCartney described Martha as:

[…] a dear pet of mine. I remember John [Lennon] being amazed to see me being so loving to an animal. He said, ‘I’ve never seen you like that before.’ I’ve since thought, you know, he wouldn’t have. It’s only when you’re cuddling around with a dog that you’re in that mode, and she was a very cuddly dog.

Martha lived until 1981 and was survived by a litter of puppies which McCartney still owns—one of them, in fact, appears on the cover of his album Paul is Live.

While the song is ostensibly a loving ode to his pet, in 2021 McCartney offered an alternative meaning: that of someone having an affair:

[…] as the song proceeds, Martha morphs into a person. As it happens, I had a relative who was having an affair and came down to London to tell me about it. Maybe for some hand-holding. […] I’m the only person who knew the song was about someone having an affair, and that gives a line like ‘When you find yourself in the thick of it’ an added layer of poignancy.

The song begins on piano, before being gradually being joined by guitars, bass, drums and eventually an orchestra as the song progresses. McCartney admitted that this song was his attempt at emulating the kind of psychedelic, complex songwriting Lennon displayed on “Happiness is a Warm Gun.” Said McCartney about the songwriting process:

When I taught myself piano I liked to see how far I could go, and this started life almost as a piece you’d learn as a piano lesson. It’s quite hard for me to play, it’s a two-handed thing, like a little set piece. In fact I remember one or two people being surprised that I’d played it because it’s slightly above my level or competence really, but I wrote it as that, something a bit more complex for me to play. Then while I was blocking out words – you just mouth out sounds and some things come – I found the words ‘Martha My Dear’.