He was a younger brother of Beppo Levi and was killed in action during First World War.

He wrote 33 papers, classified by his colleague and friend Mauro Picone[a] according to the scheme reproduced in this section.

He wrote only three papers in group theory: in the first one, Levi (1905) discovered what is now called Levi decomposition, which was conjectured by Wilhelm Killing and proved by Élie Cartan in a special case.

In the theory of functions of several complex variables he introduced the concept of pseudoconvexity[b] during his investigations on the domain of existence of such functions: it turned out to be one of the key concepts of the theory.

His researches in the theory of partial differential operators lead to the method of the parametrix, which is basically a way to construct fundamental solutions for elliptic partial differential operators with variable coefficients: the parametrix is widely used in the theory of pseudodifferential operators.