It is evident that Riemann was famous in music history and theory But in this study the writer made researches only in harmonic theories. His harmonic theory is summarized in harmonic dualism and theory of functional harmonic progression. The major triad is derived from the harmonic series and the minor triad from the mirror inversion of this series, called the "undertone series." Riemann uses the term "clang" to indicate this series. The major triad is thus termed an "overclang" and the minor triad an underclang. The tonic triad is dependent on its dominant and subdominant: every chordal structure can thus be traced back to these functional triads and each triad can be represented by one of its constituent pitches or intervals. In 20th century Schenker and Hindemith is related with the theory of funtional harmonic progression. There is similarity between Riemann's three tonal functions of tonic, dominant, subdominant and Schenker's Stufen and Hindemith emphasis on tonal center of a degree progression. In conclusion, it is quite evident that Riemann' harmonic theories are still very much alive today. It is the writer wish that this thesis may contribute to a comprehensive presentation of Riemann's theory of harmony.