The purpose of this study is to analyze four late solo piano works of Franz Liszt that all bear the name "Mephisto" in their titles, in order to examine, identify and trace the development in the use of harmonic and melodic idioms that produced non-tonal or "omnitonic" effects, on the one hand, and to emphasize the need to duly accord Liszt a recognition of historical position as the nineteenth century's most influential avant garde composer whose attitude and approach had helped to shape much of the ideal of the atonal composition of this century, on the other. Chapter One presents the issues and the purpose of this study; Chapter Two investigates the principal forces that shaped Liszt's mature compositional style; Chapter Three identifies and discusses the requisites for tonal and atonal compositions; Chapter Four analyzes the four "Mephisto" dances: Waltz no.1 (1860); Polka (1883); Waltz no.3 (1883); and Bagatelle (1885). Chapter Five summarizes the findings from this study and attempts to identify in these late works of Liszt a pattern of conscientious, continuous, purposeful and progressive use of devices toward creating musical effect that would defy the established tonal requisites and undermine the tonal orientation in the composition. This study submits that it was Liszt who had first shown a way to free music from the shackles of prescribed idiomatic constraints, and to force us the listeners to approach and appreciate music for its own sound's sake. Additionally, this study submits that this effort of Liszt should be understood and appreciated in terms of programmatic association; that is, Liszt found in the persona of Mephisto the Diablo the ideal imagery for depicting the nature of the "music of the future" where tonality would be freed from any prescribed procedural requisites.