This essay develops a theory of improvisation as practice of aesthetic sense-making. While considering all arts, references are made to many concrete cases. A topic in vogue since the XX. century, as evidenced by the great philosophers who were interested in it (Ryle, Derrida, Eco among others), improvisation, a felicitous mixture of habit and creativity, norm and freedom, is constitutive of human action. Human practices – including very well-regulated activities such as playing chess, piloting airplanes, or medicine – permit and often require it to varying degrees.Improvisation is also the true source of artistic experience. Consequently, the aesthetics of improvisation result in a philosophy of art: Art was born as improvisation. Yet improvisation has its own aesthetic dimension: that of a "grammar of contingency" in which notions such as emergence, presence, curiosity and authenticity explain the pleasures of joyful adventure and empathic involvement elicited by improvisation.