Racial theories that divided the European "race" into several "sub-races" became very prominent in anthropological communities in the early 20th century, esp. in the interwar years. Nazi Aryanism is itself an offshoot of Nordicism which was developed in the United States based on racial typologies like those of William Z. Ripley (The Races of Europe, 1899; Ripley was not actually a huge racist, as an aside, but his "tripartite" racial theory got transformed by others who were), and the Nordicism of Madison Grant (The Passing of the Great Race, 1916; Grant was a huge racist, and interpreted Ripley's typology in very harsh terms).

There is a longer history of racial theorizing (going back to around the 19th century — in Victorian anthropology, racial theories were all the rage), but the specific separation out of a specific Nordic/Aryan/Teutonic race largely begins with the authors mentioned above. The key features of this approach to race is that it subdivides "whiteness" up rather finely, notably excluding Slavs, Irish, Jews, and (in Grant's case) those in southern Europe (i.e. Italians) from the category of "valuable" Europeans. It is a typology that was popular with European racists, as well as Northeastern Americans during periods of large amounts of immigration from southern/eastern Europe. In the USA it fell out of favor after World War I and was replaced by a more "bi-color" racial typology (i.e., white vs. black, though also "yellow," "brown," and "red" in some more elaborate taxonomies, like that of Lothrop Stoddard), to the point of almost becoming incomprehensible to many Americans (i.e. the confusion over why Irish were considered a different "race").

Matthew Pratt Guterl's The Color of Race in America (Harvard University Press, 2001), does a nice job of going over the American context of these racial theories. Jonathan Spiro's Defending the Master Race: Conservation, Eugenics, and the Legacy of Madison Grant (University of Pennsylvania Press, 2008) goes into a lot of details on the formation and export of Nordicism. Robert Proctor's Racial Hygiene: Medicine Under the Nazis (Harvard University Press, 1990), describes the integration of these theories into the German context (where they get changed slightly), specifically with the aid of German academics and doctors.

In the early 19th century numerous orientalists and philologists attempted to combine Joseph Friedrich Blumenbach's race theory with the newly discovered Indo-European (at this point often called Indo-Germanic) language family. Two of the most influential works were August Wilhelm Schlegel's 1834 De l'origine des Hindous (On the Origin of the Hindus) and Christian Lassen's 1847 monumental 4 volume indische Alterthumskunde (Indian Antiquities), both of which are full of racial speculation about craniometry, facial physiology, skin color, etc. to prove that the original "Hindus" (in Schlegel) or "Aryans" (in Lassen) belonged to the white race. Both subscribe to the Aryan invasion theory, where the superior white race subjugated the dark races of the subcontinent, but eventually degenerated through miscegenation with the natives.

But Schlegel and Lassen were primarily interested in philology, not race theory. It was the Comte de Gobineau who popularized the word "Aryan" outside of orientalist circles, and made it central to his racial justification of European imperialism. His 1853 Essai sur l’inégalité des races humaines (Essay on the Inequality of the Human Races) divides humanity into three main races: black, yellow, and white (the Aryans). He further subdivides the white race into "Semeticized" whites of Southern and South-Eastern Europe, and the purely Aryan whites of "Western Civilization", in Gobineau's terminology referring to North-Western Europe and Scandinavia.

Gobineau was a popular novelist, travel writer, and public intellectual, so it was through him that "the Aryans" as the white master race first entered wider public consciousness. The label "Aryan" found particular resonance in the struggle for German unification, with its Romantic nationalist emphasis on the ancient origins of the German Heimat and Volkstum. By 1887 the term was sufficiently familiar that Franz Xaver Kießling added a clause to the constitution of his Viennese gymnastics club limiting membership to "Aryans", the first known case of an Arierparagraph. These paragraphs became common in the charters of many social and athletics clubs in the German and Austro-Hungarian empires, although they are most associated with the Nazi period. The terminology also entered the völkische Bewegung, eventually leading to Ariosophy and its influence on Nazi occultism.

On the more intellectual side, Gobineau's most influential transmitter in the early 20th century was Wagner's son-in-law, Houston Stewart Chamberlain. His 1899 Die Grundlagen des neunzehnten Jahrhunderts was a major bestseller and obligatory reading amongst the political elite of all Western nations.

Good sources include:

Stefan Arvidsson Aryan Idols: Indo-European Mythology as Ideology and Science

Robert Cowan The Indo-German Identification: Reconciling South Asian Origins and European Destinies

Sara Eigen and Joseph Larrimore (eds.) The German Invention of Race