Tomchei Temimim is the central Lubavitch yeshivah network, founded by the Rebbe Rashab in Lubavitch in 1897. This page gathers the Rebbe's letters on the yeshivah, and to its administration, students and supporters, from the 1940s to about 1970 (IK = Igros Kodesh letter number). See also the pages for its branches, such as Tomchei Temimim, Lod and Tomchei Temimim, Montreal.
What the yeshivah is for. Being a Tamim means complete dedication to Torah and mitzvos (IK 25). Even the simplest moral laws need a Divine foundation to endure, which is the yeshivah's contribution to society (IK 8338, 8940, 9826). Chabad's way joins intellect and emotion (IK 9636), and the yeshivah's task is explained at length in IK 6669. Wherever Jews settle, the first priority is a place for Torah study (IK 7552).
To the administration. There is no authority to alter the yeshivah's longstanding curriculum by adding general studies (IK 3638). Yeshiva leaders must make an honest self-accounting, especially on Chai Elul (IK 3780). Students' presence at the end of Elul and during the Ten Days of Teshuvah matters more than in Av (IK 3521). See also the letters on fundraising campaigns and enrollment (IK 4319), and on planning buildings with future expansion in mind (IK 6466).
To the supporters. Many letters are messages for the annual dinner and celebration, urging support even in hard times (IK 1347, 2403, 3209, 4914, 5010, 7940). Material support for Torah is itself made holy (IK 5995), and Chabad's tradition is self-sacrifice for pure Torah education (IK 9071). He tied the dinners to the time of year: the Alter Rebbe's yahrzeit (IK 7164, 8581), Chanukah (IK 3994, 10024, 10293, 10620), the Previous Rebbe's yahrzeit (IK 9271) and Sefirah (IK 6855). On the 70th anniversary, see IK 9433.
Buildings. On the cornerstone in Kfar Chabad, the Rebbe urged involvement with all one's resources (IK 6211; on the second wing, IK 8621). On the new central building in Brooklyn, see IK 8633, 9898.
Every siyum a new beginning. The Rebbe wrote that every siyum marks not an end but a new beginning toward higher growth (IK 8994), and that completing Torah study should lead one to rise higher and to kindle others (IK 8442).
A candle that shines. Each soul is a candle meant to shine through Torah and mitzvos (IK 9509). Every Jew inherits spiritual strength from our ancestors (IK 10422), and every part of life, even mundane acts, should be dedicated to G-dliness (IK 9158). He called for uniting around Torah study and mitzvos with renewed dedication at significant times (IK 9331).
Sources: the Rebbe's letters cited above.