Teichmüller refers to a concept in mathematics, particularly in the field of complex analysis and geometry. It is named after the mathematician Oswald Teichmüller, who contributed significantly to the study of Riemann surfaces. The Teichmüller space is a parameter space that describes the different ways a given surface can be deformed while preserving its complex structure. In addition to its geometric implications, the Teichmüller theory has applications in various areas, including dynamics, algebraic geometry, and theory of surfaces. It provides tools for understanding the moduli of surfaces and their mappings, making it a vital area of study in modern mathematics.