The foundation of the Haseki Mosque and its külliye-complex (mausoleum, soup-kitchen, hospital, sebil/fountain, medrese/high school and mektep/primary school) date from 1538-1551. It was commissioned by Haseki Hürrem Sultan (a consort – and later legal wife - of Süleyman the Magnificent) who became a ‘Haseki Sultan’ in 1538 (= a consort of the Ottoman Sultan who gave birth to a royal prince; in fact, Hürrem sultan was the first to bear this title. In the West, she is better known under the name ‘Roxelana’).
The assignment was entrusted to the newly appointed ‘baş mimarı’ (imperial chief architect) Sinan. The square mosque that he built was relatively small, with one dome; later (in 1612, under Ahmet I) an equally large dome was added, to the north of the existing building, together with the porch. Because of this extension, the mihrab (prayer niche) had to be moved to another location. The mosque was restored in 1892, after being damaged by an earthquake, and renewed in 1960-1970.

Correspondent: J.M.Criel, Antwerpen.
Sources: ‘Türkiye Tarihi Yerler Kılavuzu’ – M.Orhan Bayrak, Inkılâp Kitabevi, Istanbul, 1994 & Vikipedia/Wikipedia .

Note I put the medrese in the Istanbul medreses gallery, because it felt as a separate entity. The complex is somewhat dispersed, cut through by streets and all that.