Mathematical letters (some later published, some not)
 First second third fourth
fifth sixth seventh and eighth letters to Dixmier from 1950 to 1955 (scans).

First
second
third
fourth
fifth
sixth
seventh
eighth letters to Dixmier from 1950 to 1955 (typed).

First
second
third
fourth
fifth
sixth
seventh
eighth exchange of letters between Grothendieck and Lipman, 19691970.

Motives
letter to Serre (August 8, 1964) The English translation of a letter
from from Grothendieck to Serre which contains his first written mention of
motives. The original letter is published in Correspondance
GrothendieckSerre, Documents Mathématiques, Société
Mathématique de France, 2001.

Crystals letter to Tate (May 1966) 
A 31page letter from Grothendieck to Tate, in which the
notion of crystals was born and baptized (with a nice
``commentaire terminologique'' about the name).
It contains the conjectures, based on an analogy with the
work of MonskyWahnitzer in the affine case, on the
comparison between crystalline and de Rham cohomology.
For a firsthand historical survey of the theory (starting
with the present letter), see the article by L.Illusie
in Motives, Proceedings of Symposia in Pure Mathematics,
Volume 55, 1994, Part 1, 4370.

Motives
letter to Illusie (May 3, 1973) A letter from Grothendieck to Luc Illusie
containing remarks on motives. The original letter is published as an appendix
to an article by Jannsen, in Vol. I (p. 296) of
Motives (U. Jannsen et al. eds), Proc. Symp. Pure Math 55, AMS, 1994.

Scans of three letters from Grothendieck to Larry Breen containing
remarks on the yoga of homotopy (ncategories etc).
Letter 1
(February 17, 1975, 5 pages)
Letter 2 (July 1719, 1976, 22 pages + 4 pages of comments)
Letter 3 (April 8, 1982,
10 pages, page 4 unfortunately missing)
The same letters in a smaller size suitable for printing:
Letter 1,
Letter 2,
Letter 3.

Extract from a letter to Ronnie Brown, June 9, 1983

Anabelian
letter to Faltings (June 27, 1983)  A letter from Grothendieck to
G. Faltings in German, describing Anabelian Algebraic Geometry.
To Grothendieck's disappointment, Faltings never responded to this letter.
However, Faltings' student Shinichi Mochizuki picked up the subject years
later and proved Grothendieck's anabelian conjecture for hyperbolic curves.
This letter was later published in Geometric Galois Actions I (P. Lochak and
L. Schneps, eds., London Math Society Lecture Note Series 242, Cambridge
University Press (2000) ).
(English
translation) (
Scan of the original)
 The 1987 letter from Grothendieck to P. Blass accompanying
the prenotes for EGA V.
Collections of mathematical letters
 The GrothendieckSerre correspondence
The correspondence was first published in French by the SMF, subsequently in a
bilingual version by the AMS. The collection is in fact a selection, not the complete
correspondence. Additional letters from the correspondence
will shortly appear on this site.
 The GrothendieckMumford correspondence These
letters have been published in Volume II of Mumford's complete works.