Tomchei Temimim is the central Lubavitch yeshivah network, founded by the Rebbe Rashab in Lubavitch in 1897. This page gathers the Rebbe's letters addressed to the yeshivah and its students and events (roughly 1961–1970), most of them messages for siyumim and annual gatherings. See also the pages for its branches, such as Tomchei Temimim, Montreal.
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.