When Jefferson learned that the British had burned the Capitol and the congressional library in 1814, he was outraged and promptly offered to sell his personal library to Congress to replace the one that was lost.
He wrote to his close friend Samuel Harrison Smith on 21 September 1814 with his offer. Smith would act as his agent in the negotiations that followed. Along with his letter to Smith, Jefferson enclosed a handwritten catalogue of his library which he made in 1812. He mentioned this catalogue in his letter to Thomas Cooper dated 10 July 1812, when he wrote,
“I am making a fair copy of the Catalogue of my library, which I mean to have printed merely for the use of the library.” 
Apparently by 1812, his 1783 Catalog had become crammed with additions, interlineations, erasures, and marginal insertions such that he decided to make a new copy of his book catalogue, in which he combined and reordered several chapters, reducing the number of chapters from forty-six to forty-four. He combined Politics and Commerce into a single chapter, as he did for Gardening, Painting, and Sculpture, and gave each chapter a catalog order that he described later to the Librarian of Congress George Watterston as “sometimes analytical, sometimes chronological, & sometimes a combination of both.” 
Along with the “fair copy of the Catalogue” detailing the contents of his library, Jefferson also created an Alphabetical Index of Author’s Names which he sent to Smith later on 11 October 1814 to attach to the end of the catalogue.
After the library committee of Congress concluded negotiations in early 1815 to purchase his library for the sum of $23,950, Jefferson undertook to thoroughly review the books in his library against the catalogue, and to arrange and number the books in preparation for their delivery to Washington.
On 26 April 1815, George Watterston, the Librarian of Congress newly appointed by President James Madison, wrote to Jefferson to ask advice regarding the arrangement of the books that Watterston was to receive from Jefferson. Watterston wrote,
“I am solicitious to obtain your opinion, as a gentleman of literary taste, on the subject of arrangement . . . You will not neglect to forward
the a catalogue if you have a spare copy as I wish to have it printed as early as possible.” 
Jefferson sent his catalogue to Watterston along with the books. In his reply to Watterston on 7 May 1815, Jefferson wrote,
“ ... two methods offer themselves. the one Alphabetical, the other according to the subject of the book. the former is very unsatisfactory, because of the medley it presents to the mind, the difficulty sometimes of recollecting an author’s name, and the greater difficulty, where the name is not given of selecting the word in the title which shall determine it’s Alphabetical place . . . on the whole I have preferred arrangement according to subject; because of the peculiar satisfaction, when we wish to consider a particular one, of seeing at a glance the books which have been written on it, and selecting those from which we expect most readily the information we seek … “
“You will recieve my library arranged very perfectly in the order observed in the Catalogue, which I have sent with it. in placing the books on their shelves, I have generally but, not always, collocated distinctly the folios 4tos 8vos & 12mos placing with the last all smaller sizes.” 
Jefferson’s catalogue was used by Watterston and others to produce a printed catalogue published later that year in December 1815 as The Catalogue of the Library of the United States. To which is Annexed a Copious Index, Alphabetically Arranged.  Watterston preserved Jefferson’s subject classification and chapters, but he alphabetized the title entries within the chapters, thus destroying Jefferson’s carefully worked-out order. Jefferson complained to Joseph C. Cabell about the changes Watterston had made in his letter on 2 February 1816, in which Jefferson wrote,
“The form of the catalogue has been much injured in the publication; for although they have preserved my division into chapters, they have reduced the books in each chapter to alphabetical order, instead of the chronological or analytical arrangements I had given them.” 
The catalogue was retained by Watterston who claimed it as his personal property when he was dismissed from the post of Librarian of Congress in June 1829. In a letter to Asher Robbins, Chairman of the Joint Committee on the Library dated February 1830, Watterston wrote,
“The ms. cat. of the Liby was given to me by Mr. Jefferson, if I could save it from the printer. It was of no use to him or to the Liby & I therefore claim it as my property.” 
This manuscript catalogue has never been found and is lost, and so is this particular record of Jefferson’s original arrangement he intended for the books he sold to Congress.
A number of years following the 1815 sale, Jefferson commissioned Nicholas Philip Trist to recreate a list of the books sold to Congress in the order he had originally defined. Trist, who was the son of Jefferson’s old friend Hore Browse Trist, later married Jefferson’s granddaughter Virginia Jefferson Randolph and became Jefferson’s private secretary and executor of his estate. James Gilreath and Douglas L. Wilson write that this is not surprising since Jefferson’s thoughts during this time would have turned to book catalogs since he was actively engaged in building the University of Virginia and organizing its library.  It is unclear when Jefferson first asked Trist to undertake this task but it could have been as early as June 1821 when Trist was at Monticello.
In his letter to Jefferson from Louisiana on 18 October 1823, Trist wrote,
“I avail myself of the first opportunity that offers to return your catalogue, the absence of which will have proved, I fear, a greater in convenience than can be compensated by the copy I have made.” 
Jefferson acknowledged receipt of the catalogue from Trist the following year on 13 April 1824 when he wrote,
“The catalogues, printed and MS. were safely recieved. the last given you more trouble than I ought to have subjected you to. it is very precious to me, and I am truly thankful to you for it.” 
From Jefferson’s reply, he appears to have provided Trist a copy of the 1815 printed catalogue prepared by Watterston which he had annotated to indicate his intended order for the books. Trist then compiled a manuscript copy and sent it back to Jefferson, along with Jefferson’s annotated copy.
This 113-page Trist Catalogue manuscript was donated to the Library of Congress in 1917 by Frank Goodell, who had found it in the library he was in charge of at Camp Wheeler in Georgia. Bound with the manuscript is an unmarked copy of the 1815 printed catalog. After its acquisition, this volume was mistakenly labeled as a catalog of the library at the University of Virginia, and remained in the Library of Congress Manuscript Division until 1954 when it was transferred to the Rare Book and Special Collections Division at the Library of Congress, where it remained unnoticed at the end of the library that had belonged to Jefferson. 
In 1989, a transcription of the Trist Catalogue was published for the first time by the Library of Congress as Thomas Jefferson’s Library: A Catalog with the Entries in His Own Order.
The manuscript pages are numbered in Jefferson’s hand on rectos only. There is also a correction in his hand on page . Jefferson crossed out the name Inigo Jones and wrote “Ld. Burlington,” attributing the notes added to that edition of Palladio to Richard Boyle, third Earl of Burlington. The manuscript was later rebound by the Library of Congress. On the first page of the original fly-leaves, there is an inscription: Pearce L. Lewis of Ga., 1834, University of Va. 
Jefferson’s chapters are organized by subjects according to a general classification scheme he adapted from the second book of Francis Bacon’s The Advancement of Learning. In this book, Bacon organized all knowledge into the categories of Memory, Reason, and Imagination. Jefferson renamed these categories into History, Philosophy, and Fine Arts, and added to Bacon’s scheme by creating forty-four chapters for specific subjects.
As is the case in all of Jefferson’s manuscript book lists, the book entries follow a conventional bibliographical format used in the eighteenth-century that lists concisely the author, title, number of volumes, and size. This listing is referred to often on this website as Jefferson’s short title.
In the Trist Catalogue, each short title is preceded by a number. This number refers to its shelf position as assigned by Jefferson, rather than to its catalog order. At Monticello, Jefferson had his smaller books such as his duodecimos 12o placed on the upper shelves. He placed the middle-sized quartos 4o and octavos 8o on the ranges below them. The folios 2o were placed on the bottom shelves. So the books in each chapter were kept together on the shelves according to size. For example, in the first chapter, the numbering sequence is as follows: 1-16 duodecimos; 17-101 octavos; 102-115 quartos; 116-129 folios. A few entries begin with letters like “W” or “BB” rather than numbers. These books were particularly large and were probably kept separately.
Jefferson explained his system of arrangement in his letter to George Watterston on 7 May 1815,
“On every book is a label, indicating the chapter of the catalogue to which it belongs, and the order it holds among those of the same format. so that altho’ the Nos seem confused on the catalogue, they are consecutive on the volumes as they stand on their shelves & indicate at once the place they occupy there.” 
So Jefferson’s catalog order which he had Trist recreate relates not to their shelf order nor their size, but rather the “sometimes analytical, sometimes chronological, & sometimes a combination of both”  arrangement he had described to Watterston in 2 Mar. 1816. Gilreath and Wilson point to Jefferson’s ordering of the chapters and the individual books within each chapter as a “detailed and telling product of Jefferson’s distinctive imagination at work.”  His arrangement sought to place the titles in an order that reflected their relationship to their subject and to each other, whether historically, chronologically, or by some other analytical connection.
1. Thomas Jefferson to Thomas Cooper, 10 July 1812, Thomas Jefferson Papers, Manuscript Division, Library of Congress. Published in PTJ:RS, 5:223-224.
2. Thomas Jefferson to George Watterston, 2 Mar. 1816, ibid. Published in PTJ:RS, 9:531-532.
3. George Watterston to Thomas Jefferson, 26 Apr. 1815, ibid. Published in PTJ:RS, 8:444-445.
4. Thomas Jefferson to George Watterson, 7 May 1815, ibid. Published in PTJ:RS, 8:473-475.
5. The Catalogue of the Library of the United States. To which is Annexed a Copious Index, Alphabetically Arranged. Washington: Printed by Jonathan Elliot, 1815.
6. Thomas Jefferson to Joseph C. Cabell, 2 Feb. 1816, Thomas Jefferson Papers, Manuscript Division, Library of Congress. Published in PTJ:RS, 9:435-439.
9. Nicholas P. Trist to Thomas Jefferson, 18 Oct. 1823, Thomas Jefferson Papers, Manuscript Division, Library of Congress.
12. Bibliographic description from the Library of Congress online catalog.
13. Thomas Jefferson to George Watterston, 7 May 1815, Thomas Jefferson Papers, Manuscript Division, Library of Congress. Published in PTJ:RS, 8:473-475.
14. Thomas Jefferson to George Watterston, 2 Mar. 1816, ibid. Published in PTJ:RS, 9:531-532.