der, die oder das Semester?

Exception

-er → der

Usually 81.3% of the 2,315 common nouns ending in -er take der.

Semester breaks this rule: it is das Semester, not der Semester.

This is only a tendency. Common exceptions are family words (die Mutter, die Tochter) and das Zimmer, das Fenster.

Other exceptions die Mutter, die Tochter, die Schwester, das Wasser