Short answers, pulled from the story.
The earliest confirmed purpose-built structures are at the site of Terra Amata in France, dated to about 400,000 years ago. The site also holds the earliest evidence of artificial fire.
A ziggurat is a solid stepped tower of mud brick built in Mesopotamia, surmounted by a temple. The word is an anglicized form of the Akkadian ziqqurratum, from the verb zaqaru meaning to be high, and the buildings were described as mountains linking earth and heaven.
The Egyptian pyramid grew from the mastaba, an adobe tomb structure. The priest and architect Imhotep stacked five mastabas to create the first Egyptian pyramid, the step Pyramid of Djoser at Saqqara, and Sneferu later built the first smooth-sided pyramid.
The Greeks developed three orders by the 4th century BC, the Doric, the Ionic, and the Corinthian, recognized most easily by their columns and capitals. The Romans added two more, the Tuscan and the Composite.
Gothic architecture is traditionally said to begin with Abbot Suger, who rebuilt the west front and choir of the Basilica of St Denis from around 1135. He wrote that the old building could no longer hold the pilgrims coming to venerate its relics, and he sought stained glass to fill the space with colored light.
The Baroque was born in the painting studios of Bologna and Rome in the 1580s and 1590s, and in Roman sculptural and architectural ateliers in the early 17th century. It became the first truly global style in the arts, dominating European and Latin American art and architecture from about 1580 to about 1800.