This work consists of most of the correspondence (edited) between Andrew Erskine and James Boswell from their first meeting in 1761 until November 1762. It was printed by Chandler and published by William Flexney on April 12, 1763, an occasion described by Boswell in his journal as "the greatest day that Erskine and I ever saw".
Their joy soon turned into some regret as the letters were being ridiculed and criticized by some of their friends such as Lord Eglinton1 for being too personal (crossing the boundaries between the private and the public). Boswell's father, Lord Auchinleck, did not like them either, complaining that "though it might pass between two intimate young lads in the same way that people over a bottle will be vastly entertained with one another's rant, it was extremely odd to send such a piece to the press to be perused by all and sundry" (Letter to JB from Lord Auchinleck, May 30, 1763). On June 1, 1763, their letters were critically reviewed by the Critical Review. The review wasn't positive, but Boswell found some comfort in the fact that it was not as abusive as he had expected.
Some reviews were rather positive, though, among them one published (anonymously) in The London Chronicle on April 29, 1763 - when Boswell's papers were discovered in the 1920s it turned out that Boswell had actually written the review himself! Bonnell Thornton praised the correspondence in The Public Advertiser, and on May 24, 1763 Boswell went to see him for the first time. He was also introduced to John Wilkes and Charles Churchill (editors of The North Briton) at Thornton's on this day. Even the June edition of The Monthly Review gave the letters some praise.
The original volumes are hard to find today, but the letters themselves are all included in the recently published volume of Boswell's correspondence for the years 1757-1763. Both editions may be available via AbeBooks.