(The following have been deduced from Phoenix Wright: Trials and Tribulations and Myst IV: Revelations.)
"...on the campus of Harkely University" (Universität is feminine, so use "der" for genitive case. I've also seen this several times elsewhere.)
Just wanted to point out that in the second screenshot, we see "Vielleicht kann ich die Temperaturen innerhalb des Sichtgeräts simulieren, so dass ich es dann in Tomahna installieren kann.", which means "Maybe I can simulate the inner temperatures of the sight apparatus, so that I can then install it in Tomahna." ("des" indicates another genitive case, but what gender is Gerät? Now look back on the first page to "Das Sichtgerät zeigte nicht viel und ich überlegte, wie es zu verbessern sei." for "The sight apparatus did not show much, and I 'ponder' how to make it better." Gerät is neuter, and it is an apparatus.)
I now have the complete constructions for genitive cases:
Use des (or end pronouns with -es) for masculine and neuter nouns, and additionally, put "s" on the end of the noun if there isn't already one.
Use der (or end pronouns with -er) for feminine and plural nouns.