This thesis is a theoretical approach to study the magnetic phase transitions and exchange interactions in the spiral magnet Terbium Manganese Oxide by using group theory. First, we study the magnetic and ferroelectric transitions by considering the symmetry breaking associated with each transition. Second, we write the exchange interactions for the Mn magnetic ions in terms of the magnetic order parameters which are associated with various irreducible representations of the magnetic space group. Third, considering the exchange interactions and single ion anisotropy we examine the interactions on the whole lattice. The most general form of the exchange interactions for Mn atoms in Terbium Manganese Oxide is formulated, including nearest neighbor and next-nearest neighbor interactions. Our phenomenological model also contains antisymmetric terms which lead to a mixing of spin-wave polarizations. Finally, equations of motions for spin waves are derived.

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