Final answer:
The famous student of Hazrat Shams Tabriz was Rumi, a 13th-century Persian poet and Sufi mystic whose work had a profound impact on literature and spirituality.
Step-by-step explanation:
The famous student of Hazrat Shams Tabriz was Rumi. Jalāl ad-Dīn Muhammad Rumi, more popularly known as Rumi, was a 13th-century Persian poet, scholar, theologian, and Sufi mystic. Rumi's work transcends national and ethnic borders and he is considered one of the greatest spiritual masters and poetic geniuses in history. His poetry has influenced not just literature but the spiritual paths of countless people, and today remains crucial in understanding Sufi thought and practices.