Final answer:
Severus Snape is first seen during the start-of-term feast at Hogwarts in 'Harry Potter and the Philosopher's Stone', where he's introduced as the Potions Master.
Step-by-step explanation:
We first see Professor Severus Snape in the Harry Potter and the Philosopher's Stone during the start-of-term feast at Hogwarts, where he is introduced as the Potions Master. This happens relatively early in the book, specifically when Harry Potter is sorted into Gryffindor House and notices Snape's intense gaze upon him.
This first encounter sets the tone for Snape's character and his relationship with Harry throughout the series, which is complex and layered with mistrust and enigma.