The Rebbe's guidance on Torah study for women and girls:
What women are obligated to learn. Women are obligated to learn the laws they need — family purity, kashrus, Shabbos and all the mitzvos that apply to them (IK 2107, 9907). Their education must rest on Torah itself, not on custom alone (IK 2994). The blessing given at a girl's birth, "to Torah," reflects women's merit in Torah (IK 4156).
Chassidus too. Women are obligated to learn those parts of Torah that apply to them, including Chassidus, so that they can fulfill the constant mitzvos of faith, love and awe of G-d (IK 7555). Teaching Chassidus to women is both necessary and valuable (IK 8303), and Tanya may be taught to older girls, beginning with accessible material (IK 2375).
Gemara. How much Gemara to teach girls depends on their needs and abilities; the main focus should be practical halachah that leads to action (IK 2107, 9907).
Women's classes. Make classes engaging: include practical halachah and invite questions (IK 2697, 10518). Group study of family purity is a foundation of Jewish life (IK 7308). On Shabbos, women can learn the weekly Torah portion, Midrash and the laws of Shabbos (IK 8998). Organizing young women around Torah study builds strong homes and future generations (IK 3234), and women should take an active part in Torah study and gatherings (IK 9494).
The purpose. A Jewish woman's learning is part of her mission of making a dwelling place for G-d in daily life (IK 9374).
See also: Parenting – Raising daughters; Torah study – Learning practical halachah.