The beauty and artistry of the variation form were fully developed and represented in the nineteenth century. The treasures of nineteenth century piano variations are a significant part of the total piano repertoire. The main goal of this dissertation is to show how various composers of the nineteenth century used the variation form to project their imagination and coloring of a simple melody. They used many different techniques to vary melodies and create their own music. Beethoven's Piano Sonata No. 12 in A-flat Major Op. 26 breaks with the conventional sonata design by using variation form instead of sonata-allegro form for the first movement, and having no movement in sonata-allegro form. Chopin's Variations Brillantes on "Je Vends des scapulaires" Op. 12 and Henri Herz's Variations on 'Non piu mesta" from "La Cenerentola" shows how they applied their art to composing variations on opera themes. Mendelssohn's Variations Serieuses Op. 54 was a reaction against the salon music in the 19" century. Schubert applies the variation form to his Impromptus in B-flat D. 935 No. 3. Schurnann's Symphonic Etudes represents a perfect example of the arts of variation, using counterpoint, and special coloring; and Faure's Theme and Variations Op. 73 represents one of the most outstanding nineteenth-century works in variation form. As a traditionalist in the nineteenth century, Brahms favored the variations over other classic forms. I have performed three of his most important sets of variations: including Variations on a theme by Schumann Op. 9, Variations on a Theme by Handel Op. 24, and Variations for two pianos on a Theme by Haydn Op. 56b. The variations listed above were divided into three recitals. These variations represent a very important part of the piano music of the nineteenth century. By discovering, preparing, and performing these wonderful works, I have grown, both as a pianist and as a musician.