Short answers, pulled from the story.
The Austrian school originated in Vienna in 1871, when Carl Menger published Principles of Economics. The school gets its name from members of the German historical school, who coined the term during the late 19th-century Methodenstreit to characterize the Viennese economists as provincial outsiders.
Carl Menger, Eugen von Böhm-Bawerk, and Friedrich von Wieser are considered the first wave of the Austrian school. Menger's 1871 Principles of Economics is generally regarded as the founding work; Böhm-Bawerk and Wieser developed the school's theories of capital, interest, and opportunity cost.
Praxeology is Ludwig von Mises' term for his method of deriving economic truths from basic axioms of human action, without relying on empirical observation or statistical analysis. Mises laid out his full praxeological system in Human Action, published in English in 1949.
The economic calculation problem, first developed by Ludwig von Mises in his 1920 essay, argues that socialist planned economies cannot efficiently allocate resources because, without price signals from freely exchanged capital goods, planners lack the information needed to make rational economic decisions. Friedrich Hayek expanded the argument in works including The Road to Serfdom.
Friedrich Hayek shared the 1974 Nobel Memorial Prize in Economic Sciences with Gunnar Myrdal. His award contributed to renewed public interest in the Austrian school, which had been largely sidelined by mainstream economists favoring mathematical modeling since the mid-20th century.
Some economists and political scientists argue that Bitcoin reflects Austrian principles including sound money, decentralization, and resistance to currency debasement. Writers such as Saifedean Ammous and Nick Szabo used Austrian analysis to explain why Bitcoin's fixed cap of 21 million coins prevents the kind of supply inflation that destroyed the Rai stone currency of Yap in the 1870s.