The purpose of this study is to analyze sets of variations on Paganini's theme by three twentieth-century composers: Ferruccio Busoni, Ignaz Friedman, and Robert Muczynski, in order to examine, identify, and trace different variation techniques and their applications. Chapter 1 presents the purpose and scope of this study. Chapter 2 provides background information on the musical form "theme and variations" and the theme of Paganini's Twenty-fourth Caprice, Op. 1. Chapter 2 also deals with the question of which elements have made this theme so popular. Chapters 3,4, and 5 examine each of the three sets of variations in detail using the following format: theme, structure of each variation, harmony and key, rhythm and meter, tempo and dynamics, motivic development, grouping of variations, and technical problems. Chapter 6 summarizes the findings from this study and attempts to compare those elements among the three variations. Special attention is given to the application of the motivic cells, which are drawn from the original Paganini theme, in the development of succeeding variations. This study shows how these motivic cells contribute to the construction of new motives and melodies in each variation. Additionally, this study attempts to examine each composer's efforts in expanding variation procedure to the areas of structures and tempo markings in succeeding variations.