Should the young man propose marriage again to his female colleague who told him she does not love him because she is attached to someone else, or should he distance himself from this university department, especially since she still looks at him, and he is affected by her presence and absence?

What is known as a love relationship between young men and women is not sanctioned by Islamic law. What is sanctioned is for a man to propose to a woman he wishes to marry, through her legal guardian. This relationship must be severed, and places of intermingling should be avoided. If you can move to another place at the university to avoid her, then do so. If the girl is religious and you are capable of marriage, then there is no harm in proposing to her through her guardian. However, if you are unable to marry her, then you must strive to remove her attachment from your heart by seeking Allah's help, cutting off the causes of attachment, and occupying your time with beneficial deeds.