Short answers, pulled from the story.
Muhammad arrived in Medina in 622 and built a simple structure of unbaked brick that measured roughly 53 by 56 meters. This early mosque featured a rectangular courtyard surrounded by a shaded portico supported by palm trunks on the north side.
Caliph al-Walid I rebuilt the Great Mosque of Damascus starting around 707 and introduced the mihrab, a concave niche in the qibla wall that became a standard feature for all future mosques. He also experimented with vaulting techniques borrowed from Iranian architecture, creating barrel vaults resting on diaphragm arches.
Architects in Samarra developed the four-centred arch, a sophisticated variation of the pointed arch used in monuments like the Qasr al-Ashiq palace. They also created new decorative styles using stucco and plasterwork to render earlier vegetal motifs into abstract forms known as the beveled style.
Caliph Abd al-Malik commissioned the Dome of the Rock in Jerusalem during the late seventh century. Its octagonal layout likely drew inspiration from earlier Byzantine martyria such as the Church of the Kathisma.
Seljuk patrons transformed Islamic architecture across Iran and Central Asia using baked brick for both construction and decoration starting in the tenth century. The Jameh Mosque of Isfahan received four large iwans around its courtyard in the early twelfth century, establishing the four-iwan plan.