The relationship between the two men is remarkable for both personal and scientific reasons. Mittag-Leffler met Volterra for the first time when Volterra was a brilliant young student of Ulisse Dini in Pisa. He was soon captivated by the creativity and the skills of the young man and eventually became his mentor. Mittag-Leffler, who was at the center of a major scientific network, introduced Volterra to the major mathematicians of that time. In a few years, Volterra became the most prominent Italian mathematician and forged his own network of scientists all over Europe and even in the United States. Volterra was one of the first major European mathematicians to visit the U. S. Despite their difference in age, both men developed a deep and faithful friendship, and their letters reflect the variety of themes of their exchanges. Of course, mathematics was the most prominent, and both men often used the letters as a first draft of their ideas and the addressee as a first judge of their soundness.

Besides mathematics, they also touched upon many aspects of both private and public life: matrimony, children, holidays, politics, and so on. This vast set of letters affords the reader a general overview of mathematical life at the turn of the 19th century and an appreciation of the European intellectual spirit which came to an end, or at least suffered a drastic turn, when the Great War broke out.

Volterra and Mittag-Leffler's exchanges illustrate how general analysis, especially functional analysis, gained a dramatic momentum during those years, and how Volterra became one of the major leaders of the field, opening the path for several fundamental developments over the following decades. Through the letters, the reader can follow the institutional career and scientific activity of both Volterra and Mittag-Leffler, who shared many details about their lives.

The four editors are all specialists in the history of mathematics of the considered period. An extensive general introduction to the correspondence explains the context and the conditions in which it was developed. Moreover, the original letters are annotated with a large number of footnotes which provide a broader cultural picture from these captivating documents.