Linear Fractional Transformation, also known as a Möbius transformation, is a function of the form f(z) = (az + b) / (cz + d) where ad - bc ≠ 0, mapping the extended complex plane to itself. It preserves the cross-ratio of four points and is instrumental in complex analysis, geometry, and dynamic systems due to its conformal properties and ability to transform circles and lines into circles or lines.