The book is a work in two volumes: Maria Gaetana Agnesi, "Instituzioni Analitiche ad uso della gioventù italiana", Milan 1748. The title roughly translates to "Foundations of Analysis for use by Italian youth". As the title suggests, this is a textbook, and it was written in the vernacular rather than in Latin.
Google's scan of the first volume (tomo I) is here, a scan of the second volume (tomo II) is here. An English translation by the Rev. John Colson was published in London by Taylor and Wilks in 1801. A scan of it can be found at Google. According to the editor's note at the front of the book, Colson was Lucasian Professor of Mathematics at the University of Cambridge. It further notes:
That learned and ingenious man, who had obliged his Country with an English Translation of Sir ISAAC NEWTON's Fluxions [...] found, after all, the Analytical Institutions of Agnesi to be so excellent, that he was at pains of learning the Italian Language, at an advanced age, for the sole purpose of translating that work into English; that the British Youth might have the benefit of it as well as the Youth of Italy.
A curious detail on the title page of Instituzioni Analitiche is that it does not mention a printer. While other books published in Milan at the same time carried a note such as this one:
In Milano, nella Regia Ducal Corte, per Giuseppe Richino Malatesta Stampatore Regio Camerale. Con licenza de' Superiori. 1748.
identifying the printer as Giuseppe Richino Malatesta (1694-1793), from a local family of printers active from the 16th through the 18th century, it simply has a notice that reads:
In Milano, MDCCXLVIII. Nella Regia-Ducal Corte. Con Licenza de Superiori.
which translates to "In Milan, 1748. In the Royal-Ducal Court. With License of the Superiors." Looking into this, I learned that Maria Agnesi apparently had a printing workshop set up at her family's house to produce the book there, which could explain the omission of the printer's name.
Paula Findlen, "Calculations of faith: mathematics, philosophy, and sanctity in 18th-century Italy (new work on Maria Gaetana Agnesi), Historia Mathematica, Vol. 38, No. 2, May 2011, pp. 248-291 (online):
She was so concerned about the production of her textbook that she asked the printer Giuseppe Richini to set up his press inside Palazzo Agnesi so that she could personally supervise the technical difficulties of typesetting mathematical characters and laying out the formulas well on every page.