Explain how sociological theory developed in nineteenth-century Europe?

Sociology was born in the nineteenth century. The idea of a "science" of society—that one could use scientific methods to solve social problems—is most closely associated with the French thinker Auguste Comte. Comte was a positivist, meaning he believed in human progress and in the use of knowledge, particularly scientific knowledge, to further this progress. Comte envisioned sociology following the rigor of the physical sciences and thought of it as a kind of "social physics." He felt it should employ scientific methods (experiment, the use of quantitative analysis, and so on).
Another pioneering sociologist of the nineteenth century was Herbert Spencer. Spencer's ideas were more in line with classical liberalism than Comte, who trended toward utopian thought. Spencer was influenced by Charles Darwin and his theory of evolution. He saw in this idea the possibility for social evolution.
Later nineteenth century work built on these founders, and sociology departments appeared in universities in the last decade of the century. A classic sociological text is Emile Durkheim's study of suicide (1897), which uses statistical analysis and understandings of psychology very effectively. It makes recommendations for institutional change, something that would become a hallmark of sociological thought in the early twentieth century.