This thesis examines the unique musical and cultural elements particular to jazz improvisation. The topics of scales, melody, voicings, harmony and rhythm are examined in separate chapters with over two hundred notated musical examples used to demonstrate the materials in their context. This thesis also seeks to explain the relationships between these elements and presents the material material in a form applicable to improvisation. In its relatively short history jazz has developed many unique musical and cultural elements. The fact that most of these musical elements have been developed in an improvised environment means that the complexity of the harmonic, melodic and rhythmic material presents more than an academic challenge for the studentof this music. To play jezz rrquires a deep understanding of the complex relationships that exist between melody, harmony and rhythm. This must go beyond an academic understanding because the practical application of this knowledge ultimately determines whethe the elements can be used spontaneously in improvisation. To explain the theoretical material that underlies jazz improvisation, various types of musical shorthand and complex techniques of cross-referencing have evolved. Until more recently most of these techniques have been kept within the profession and were shrouded in mystery, with most information being passed directly from master to student. The relative lack of literature on the theoretical components of jazz, and the fact that most of its finest examples only exist in recorded form, have exacerbated this situation. In the last decade or so several books have been Written in an attempt to decipher jazz. The best of these works contain a large academic component with an emphasis on using the material in the context of improvisation. The theoretical complexity of jazz rivals any other western or non-western from of music, but the way in which it has been taught is based on the African tradition of aural learning through imitation. As jazz has grown in complexity, the tradition of learning improvisation solely by imitation has proven to be inadequate. The modern trend towards the blending of theoretical, practical and intuitive learning, has created a need to find new ways of organising the ever increasing material. This thesis seeks to examine the elements of jazz and categorise and organise the information in a more efficient way. The thesis is divided into chapters exploring scales, melody, voicings, harmony and rhythm. The subject of scales is explored with reference to traditional and extended structures and their particular relationship to harmony. To describe the relationships between scales and chords several charts and diagrams are employed, with parallel and derived approaches as a basis. Jazz contains many unique ways of generating and structuring voicings, with 4-way close, drop 2, slash chords anbichords, pentatonic derivatives, upper structures and quintal structures forming basis of this study. The similarities and differences between European classical harmony and extended jazz harmony are explored, with an emphasis on the techniques found in jazz. To explore this connection many written examples show the gradual introduction of harmonic density, from simple four-part writing through tro the of upper structure, alteration, substitution, superimposition and polyphonic elaboration. Basic reharmonisation and techniques of variation in chord progressions are explored, with a comprehensive study of chord substitution. Transcribed examples from the jazz repertoire are used to trace melodic and harmonic chromaticism, with reference to the parallel developments in rhythm. The use of polyrhythm, displacement, rhythmic grouping and metric modulation are examined with an emphasis on the parallel developments in harmony and melody. This thesis also contains several essays that examine the relationship between jazz and 20th-Century music the evolution of chromaticism in jazz, and the unique culture of jazz improvisation.