The Piano Sonatas of Rodolfo Halffter (b. 1900, Madrid, Spain) represent an important body of literature not widely known nor understood for their historical importance and Spanish heritage. The entire development of Halffter's compositional style, which embraces three periods of composition, may be traced through these sonatas. The modes of composition may be seen not to be separate and distinct but as having inter—relationships which therefore affect the outcome of Halffter's final dodecaphonic technique. The culmination of his serial method is found in the Tercera Sonata, op. 30. At first glance, this work appears to be a radical departure from the former styles. However, a more in-depth study reveals this sonata to be the logical outgrowth of earlier compositional techniques, thereby blending diverse, eclectic elements into a unique and homogenous application, all Halffter's own. Forced to flee his native country in 1939, Halffter became the first composer in Mexico to use twelve-tone techniques. Together with Carlos Chavez, he exerted great influence on the present generation's group of Mexican composers. Halffter today remains a crucial link in the continuation of the Spanish tradition as exemplified by his former mentor, Manuel de Falla. A brief explanation of Falla s theory of resonance including sketches in Falla's handwriting as well as portions of the unpublished analysis of Halffter's Tercera Sonata are presented, perhaps for the first time. This study reveals how Halffter manipulates many Spanish elements which are found in the ancient cante iondo and the string tunings of the guitar in addition to the use of acciacaturas and the internal rhythm of Domenico Scarlatti into a personalized idiom which remains apparent throughout all his compositional styles. An analysis of Halffter s Tercera Sonata shows that the final period is characterized by a unique blending of Falla's "apparent poly-tonality" with the twelve-tone system of Arnold Schoenberg.