Improvisation is increasingly being recognised as central to a wide range of human activities. Yet despite its centrality, few have inquired into the underlying structure of improvisation as such. Beginning with improvisation in music, this thesis develops a hermeneutic-topological account of improvisation as an attending and responding to the situation in which one finds oneself. Working between music theory and philosophy, the thesis thereby advances an account of the structure of improvisation that is shown to be at work in musical performance but also in the conversational structure of understanding evident in the work of German philosopher, Hans-Georg Gadamer.