Source: University of Leiden, BPL 246/ Boswell 1763/1764). The letter is addressed to Abraham Gronovius, (1695-1775), Librarian of the University of Leiden. Gronovius was a former fellow student of James Boswell’s father. The letter is undated, but it must have been written some time between 21 December 1763 and 7 January 1764. 

This is a transcription of the letter:

                                     Worthy and Dear Sir.

After having past a forthnight in the gay world at the Hague, where I have received the greatest civilitys from my Re::lations, and from many other people of distinction, I returned last night to Leyden. I am happy to embrace your kind invitation of passing a Saturday with you. I would wish to employ the morning in copying the notes on the Greek Lyrics; so have sent you this note to let you know that I will wait upon you as soon as you give me permission.         I am

With great respect/ and esteem/ Worthy & Dear Sir

Your much obliged and/ obedient Humble Servant

James Boswell

The image shows Boswell around the time he wrote the letter (source).