The book that Commander Lawrence is reading to the Marthas and the children is Treasure Island, written by Robert Louis Stevenson in 1883.
The title of this episode, "Mayday," is the name of the secret underground rebellion against the Gilead regime. The name comes from the military and aviation emergency procedure word in radio communications. In Margaret Atwood's source novel, Offred reflects on the origins of the word: "Mayday used to be a distress signal, a long time ago, in one of those wars we studied in high school. I kept getting them mixed up, but you could tell them apart by the airplanes if you paid attention. It was Luke who told me about mayday, though. Mayday, mayday, for pilots whose planes had been hit, and ships--was it ships too?--at sea. Maybe it was S O S for ships. I wish I could look it up. And it was something from Beethoven, for the beginning of the victory, in one of those wars. 'Do you know what it came from?' said Luke. 'Mayday?' 'No,' I said. 'It's a strange word to use for that, isn't it?...' 'It's French,' he said. 'From m'aidez.' Help me."
In the flashback scene at the start of the episode when June is being detained, she sees Brianna, one of her fellow handmaids being escorted away.