This is a Dover reprint of a book first published in 1920 collecting articles first published between 1916 and 1918 in The Monist, a philosophical journal with a special interest in the philosophy of science. (It seems that The Monist is still being published , though it no longer specializes in science-related topics.) The title doesn't quite represent the contents of the book. First of all, it's not clear that these are "the" early manuscripts of Leibniz. Second, there are several other things in the book.
After an introduction by J. M. Child, the book opens with two texts written by Leibniz in which he recalls the origins of the calculus. The first, from 1703, seems to have been intended as a postscript to a letter to Jakob Bernoulli, but never actually sent. The other, "Historia et Origo Calculi Differentialis", which may have been written late in Leibniz's life as a response to the publication, in England, of the Commercium Epistolicum, i.e., in the context of the controversy with the mathematicians of England about the true creator of the calculus. It remained unpublished, however, probably because Leibniz died before being able to see it to press.
Next come a selection of early manuscripts of Leibniz (dated 1673 to 1675), and a second group of manuscripts (between 1676 and 1677, plus an undated manuscript). These are followed by two essays by C. I. Gerhardt, the original editor of the manuscripts in question. All of the texts (including Gerhardt's!) are extensively annotated by the translator and editor.
The introduction and the articles by Gerhardt are rather dated, at least in the sense that they seem very concerned with the priority debate between Newton and Leibniz. From our perspective, this seems a little quaint: most historians, today, have no doubt that Leibniz and Newton made their discoveries independently of each other. Of course, both built on the work of other authors (which J. M. Child seems concerned to establish with respect to Barrow). Few historians today would think that these are really important questions; we are far more interested in tracing the development of ideas than in establishing anyone's priority.
The texts included here remain interesting, however. They will be, no doubt, included in Leibniz's complete works, which will eventually supersede this volume. But Leibniz's Sämtliche Schriften und Briefe are hard to find, mostly in German and Latin, and still incomplete. (But note that various portions of this are now available in digital form, including parts 3, 4, and 5 of the Mathematische Schriften.) In English, there is the Yale Leibniz, but so far this only includes three (quite expensive) volumes, only one of which is (somewhat) related to mathematics. This Dover volume is much more easily accessible. inexpensive, and in English. For those interested in seeing what Leibniz's early work looked like, and what he had to say about it later in his career, this book will serve well.
Fernando Q. Gouvêa is professor of mathematics at Colby College, where he teaches, among other things, a course on the history of mathematics.