The Rebbe's letters on Kabbalah and the inner dimension of the Torah, gathered by the questions people actually ask. Each page summarizes his guidance and cites the letters (IK = Igros Kodesh letter number).
The inner dimension of the Torah (Pnimiyus HaTorah) — A mitzvah of our generation, essential for bringing the redemption, and requiring expertise like any other part of Torah.
Studying Kabbalah — An obligation and a privilege, learning it through Chassidus first and only from the works Chassidus cites, and caution with controversial books.
Tzimtzum: literal or not — The historical views, Chabad's position that it is not literal, the Vilna Gaon and Rabbi Chaim of Volozhin, and what it means for Divine Providence.
Authority of the Arizal's teachings — Whether the Arizal's Kabbalah is to be accepted in its entirety.
Related pages elsewhere: Torah study – Learning Chassidus; Faith and Chassidus – Chassidus (general); Jewish outreach – Spreading Chassidus (hafatzas hamaayanos).
In short: The Rebbe taught that learning the inner Torah is not optional in our generation but a mitzvah and a preparation for Moshiach — reached through Chassidus, which makes the teachings of Kabbalah understandable and safe, and only then through the Kabbalistic works it cites. He held firmly to the view of the Alter Rebbe that the tzimtzum is not literal, so that G-d fills all existence even now, and warned against taking Kabbalah literally or learning it from unreliable sources.