This is an a-typical mosque in its architecture, and particularly the adjacent türbe (tomb) for a famous Tripolitanian Sheikh Azfir, member of the Shazeli dervishes, is a wonderful building. Next to it is a library that could not be visited, but the türbe turned out to be opened. I enjoyed seeing a fire engine in a windowsill, waiting for a kid to play with while a parent prayed. The tomb is by architect D’Aronco.
The mosque itself is actually part of a tekke, the Ertuğrul Tekkesi. From the Wikipedia: “A late Ottoman period mosque, it is constructed as a külliye consisting of a tekke, guest house, türbe, fountain, and library in addition to the mosque. The construction of the mosque and the külliye complex was commissioned by Ottoman sultan Abdul Hamid II, and finished in 1887. It is dedicated to the founder of the Medeni branch of Shadhili (Turkish: Şaziliye) tariqa, a Libyan sufi, Sheikh Hamza Zafir. The mosque is named after Ertuğrul Gazi, the father of the founder of the Ottoman Empire, Osman I, as a commendation to him. The name also comes from the Ertuğrul regiment, a royal palace guard regiment which comprises Turks from the Domaniç region. Initially the complex only consisted of the mosque, tekke, and the guesthouse. After the death of Sheikh Hamza Zafir in 1903, his türbe was constructed next to the mosque by the Italian architect Raimondo D'Aronco between 1905 and 1906. The library and the fountain were also added in this expansion. After the passing of Sheikh Hamza Zafir, his two brothers Muhammed Zafir Efendi and Beşir Zafir Efendi became the sheikhs of the tekke. They are also buried in the türbe next to their elder brother. “

Also from the Wikipedia, concerning the religion of Sultan Abdülhamid II: "Sultan Abdul Hamid II was a practitioner of traditional Islamic spirituality. He was influenced by Libyan Shadhili Madani sheikh, Muhammad Zafir al-Madani whose lessons he would attend in disguise in Unkapani before he became Sultan. Abdul Hamid II asked Sheikh al-Madani to return to Istanbul after he ascended the throne. The sheikh initiated Shadhili gatherings of remembrance (dhikr) in the newly commissioned Yıldız Hamidiye Mosque; on Thursday evenings he would accompany Sufi masters in reciting dhikr. He also became a close religious and political confidant of the Sultan. In 1879 the Sultan excused the taxes of all of the Caliphate's Madani Sufi lodges (also known as zawiyas and tekkes). In 1888, he even established a Sufi lodge for the Madani order of Shadhili Sufism in Istanbul, which he commissioned as part of the Ertuğrul Tekke mosque. The relationship of the Sultan and the sheikh lasted for thirty years until the latter's death in 1903."