Final answer:
The poet wants the woman to read a book that will remind her of her youth and beauty when she was loved by the speaker.
Step-by-step explanation:
The book that the poet wants the woman to read when she is older is not explicitly mentioned in the poem 'When You Are Old'. However, the poem suggests that the poet wants the woman to read a book that will remind her of her youth and beauty when she was loved by the speaker. The poet wants her to remember the passion and admiration she once inspired, and perhaps find solace in those memories in her old age.