If you dream of a poem or any part of a poem, it indicates that you are entering a business that will provide you with a wealth of knowledge. Additionally, it may symbolize success and profit in your trade or profession. This dream is a positive sign for your future, suggesting that the path you are on will lead you to success.
From Imam Muhammad Ibn Seerin's Dictionary of Dreams According to Islamic Inner Traditions â entry "Poem" (page 334).
Memorizing a poem or a verse from a poem in a dream means engaging in a business from which one will acquire great knowledge, or it could mean profits or success in whatever trade one chooses to practice. Ifone sees himself in a court of justice reciting poems for money in the dream, it means that he will give a false testimony. If he recites a poem for a gathering in a dream, it means that he will relate a wise saying, though he himself inclines to hypocrisy. If one sees himself listening to a poem in a dream, it means that he will associate himself with a group of people who do not foster the truth. In a dream, poems also represent falsehood or vain talk. Reciting a poem or listening to one and memorizing its verses in a dream means that one should take heed to what it says. If the poem one is listening to in his dream contains wisdom or a divine revelation, then it does mean good. Composing a poem, or memorizing it in a dream also means losing one's status, dismissal from one's job, weakness in one's religious adherence, suffering from depression, adversities, suffering from slander by one's enemy, or it could represent a crafty ploy. If one composes a defamatory poem or a satirical poem in a dream, it means that he slanders others for fun or profit. If it is lauding someone, then it means that he will become poor. If he sings his poem with a melody in the dream, it represents a satirical attitude toward someone, doubt about someone, or failure to complete one's work. (Also see Poet)
Note: Islamic dream interpretation depends on the dreamer's circumstances and state. This is a general guide drawn directly from the source book.