This translation is based on the text of the letters edited by R. A. B. Mynors (Oxford, 1963), which is faithfully reproduced in the Loeb edition (ed. B. Radice, 1969). It rests on three separate manuscript traditions, which Mynors labels alpha, beta, gamma, and which are popularly known as the Nine-book, Ten-book, and Eight-book versions.
The Nine-book tradition is represented by two ninth-century manuscripts M and V, and V does not survive after V 6, leaving M as the sole representative of this tradition for V 7 to IX. The Ten-book tradition (beta) provides the sole evidence for Book X; no manuscript survives after V 6, so that we are dependent on printed editions for the rest. The Eight-book version (so called because it does not contain Book VIII) has no complete surviving manuscript, and provides the least reliable readings of the three. Mynors helpfully prefaces his edition with a book-by-book survey of the available evidence from the three traditions. The section numbers of Mynors’ text are given in the margins. The existence of the letters as we have them is attributable to the heroic endeavours of the Italian and French humanists. They assembled them from widely dispersed texts of the three traditions. There is an enlightening brief account by Reynolds in L. D. Reynolds (ed.), Texts and Transmission (Oxford, 1983), 316-22. (Pliny the Younger, Complete Letters, A new translation by P.G. Walsh, OUP Oxford 2009)
From an earlier, classic collection:

Sources of the Text
For the first nine Books, we have three distinct sources, viz. (a) MSS. containing Books I.-V., of which the best are R (Florentinus Ashburnhamensis R. 98 olim Riccardianus), tenth century, F (Laurentianus S. Marci 284), tenth-eleventh century; (6) MSS. containing Books I. -VII. and IX., all of the fifteenth century, of which D (Dresdensis D. 166) is representative; © MSS. containing nine books, of which the best is M (Laurentianus 47. 36). V (Vaticanus 3864) is closely akin to M, but contains only Books I.-IV. The text of Book X. depends on a lost MS. which contained also the first nine Books. While this was still extant at Paris, copies of it by different hands were used by Avantius of Verona for his edition of 1502, and by Aldus in 1508. But while the Aldine edition gave the tenth Book entire, the first forty Letters are for some reason missing in that of Avantius. A MS. of these Letters has been discovered by Hardy in the Bodleian Library, which appears to be the actual copy from which Aldus printed.
In France Giovanni Giocondo (c. 1433 – 1515) a Dominican priest, claimed to have discovered a manuscript of Pliny the Younger’s letters containing copies of his correspondence with Trajan. Two Italian editions of Pliny’s Epistles were published by Giocondo, one printed in Bologna in 1498 and one from the press of Aldus Manutius in 1508.