Max Weber (1864- 1920) is perhaps best known of his work on the Protestant Ethic and the Spirit of Capitalism. His views have been much debated but the key idea in Weber was that there was a link between the rise of capitalism and an ethos of self control associated with Protestant reformation. By stressing the cultural, rather than the economic, dimension Weber has often been seen as anti Marxist camp but things are more complicated than that, Weber was choosing to focus on the cultures we create rather than dismissing structural and other issues (see Giddens 1970 below if you want to carry this further ).

Weber is also much known for his later work on authority. Put briefly he identified three types of authority: rational (rule based); traditional and charismatic. All three were ideal types – or generalisations. In practice all aspects of authority were interrelated and dynamic, though there was a tendency towards rational authority in the modern state.

Weber has been hugely influential in our understanding of social theory but his work is difficult to categorise. You can find some self styled Weberian analyses (for example Bocock, 1971 below) but he offers more a way of thinking about social research rather than a particular method or methodology. Key to this perspective is a concern for what may today recognise as interdisciplinarity, criticality and and interest in the consequences of cultural beliefs.

References

Bocock, R. (1971) The Ismailis in Tanzania: A Weberian Analysis, The British Journal of Sociology, 22, 4, 365-380.

Giddens, A. (1970) Marx, Weber, and the development of capitalism, Sociology,4 , 3, 289–310.

Weber, M. (1922) Economy and society; an outline of interpretive sociology. (various editions or simply search Internet archive at archive org) https://archive.org/details/MaxWeberEconomyAndSociety

Weber, M. (1904 / 1905) The Protestant Ethic and the Spirit of Capitalism.

https://archive.org/details/protestantethics00webe

And for a simplistic overview you could try