The Yunus Emre Camisi, 1349, the oldest building in town, from the Karamanoğlu period. The Wikipedia has some information about this dynasty: Beylik of Karaman or of Karamanoğlu (Karamanoğulları in Turkish plural), also called the Karamanid Dynasty or the Karamanids, was an Anatolian Turkish Beylik state centered in south-central Anatolia, around the present-day Karaman Province. From the 13th century until its fall in 1467, Karamanoğlu was one of the most powerful states in Anatolia.
Curiously I could speak with the imam in my own language, Dutch, as he had lived in Vlaardingen till he was 12.

Adjacent to the prayer hall of the mosque, there is a türbe (mausoleum) that is said to be the burial place of Yunus Emre, the famous 13th/14th century poet and Sufi mystic, who lived in Karaman for a number of years. (Note that there are six other and widely dispersed localities disputing the privilege of having his tomb within their boundaries).