Short answers, pulled from the story.
Carl Menger published Principles of Economics in Vienna on the 1st of January 1871. This publication marked the birth of a distinct economic tradition that would later be called the Austrian school.
The three men who formed what historians call the first wave of Austrian economists are Carl Menger, Eugen von Böhm-Bawerk, and Friedrich von Wieser. These figures introduced subjective value theory, capital theories, and opportunity cost concepts respectively.
Gustav von Schmoller used the label Austrian during the Methodenstreit dispute of 1883 to dismiss Menger and his followers as provincial outsiders. The term implied their approach was narrow and unscientific before adherents eventually adopted it themselves.
Friedrich August von Hayek shared the 1974 Nobel Memorial Prize in Economic Sciences with Gunnar Myrdal. This award brought renewed attention to the Austrian tradition after decades of obscurity.
Ludwig von Mises published Human Action in English on the 1st of January 1949. He argued that deductive thought experiments yield irrefutable conclusions derived from the axiom of purposeful human action.
The Austrian theory identifies bank credit issuance at artificially low interest rates by fractional reserve banks as the root cause of economic fluctuations. This policy causes businesses to invest in unsustainable roundabout production processes leading to an artificial boom followed by a necessary bust.