Will there be a change in the way we study Torah when Moshiach comes?

The primary change will be in the dimension of Torah that we study.  Torah study is generally divided into two dimensions. The "revealed" Torah deals mainly with physical, concrete principles such as the details of Jewish law and practice.  The "hidden" dimension is the mystical, abstract philosophy of Torah, found in the study of Zohar and Chassidic teachings.

The revealed Torah covers the practical laws of daily living, the intricate details of halacha, what is permitted and what is forbidden.  It also deals with negative matters such as laws of damages, disputes and lawsuits. Prior to the Redemption, this field of Torah is most commonly studied.  The hidden dimension of Torah involves concepts such as the evolution of spiritual worlds, the divine attributes, and the G-dly energy that permeates our world.  In the time of Geulah, this is the dimension that we will spend most of our time studying.

The hidden dimension of Torah is studied before the Redemption as well.  However, in order to understand it, it must be cast in physical, concrete terms.  In the future, we will study the pure mystical dimension of Torah, without having to dilute it into physical terms.

The difference between the two eras is that during exile, there is a great deal of evil present in the world, which we must combat. Every time we learn in Jewish law about what is forbidden and what is permitted, we weaken the powers of evil and give strength to the good.  When Moshiach comes, all impurities will be removed from this world and we will no longer need to sort between good and evil.

In the time of Redemption, the world will return to its pristine state. G-dliness will be openly revealed in the world, and our primary focus of study will be on the mystical dimensions of Torah, which help us understand G-d's very Essence.

(Igeret Hakodesh, ch. 24.  Torat Menachem, 5748, vol. 1, p. 392.  See also Introduction to Zohar, by Rabbi Dov Ber of Lubavitch)