This paper explores the theory of generalized Donaldson-Thomas invariants and their wall-crossing formulas in the context of non-commutative 3-dimensional Calabi-Yau varieties. It introduces a framework for stability structures, which encode polarization through stability conditions on triangulated categories. The paper defines motivic Donaldson-Thomas invariants, which take values in certain Grothendieck groups of algebraic varieties. These invariants are related to the counting of semistable objects in the category, and their behavior under wall-crossing is described by a multiplicative wall-crossing formula. The formula is expressed in terms of graded Lie algebras and involves the study of symplectic structures and automorphisms. The paper also discusses the relationship between these invariants and cluster transformations, as well as their connections to other areas of mathematics, including non-commutative geometry, algebraic geometry, and mathematical physics. The results are supported by various conjectures and examples, and the paper concludes with a discussion of the implications of these results for the study of Calabi-Yau categories and their invariants.This paper explores the theory of generalized Donaldson-Thomas invariants and their wall-crossing formulas in the context of non-commutative 3-dimensional Calabi-Yau varieties. It introduces a framework for stability structures, which encode polarization through stability conditions on triangulated categories. The paper defines motivic Donaldson-Thomas invariants, which take values in certain Grothendieck groups of algebraic varieties. These invariants are related to the counting of semistable objects in the category, and their behavior under wall-crossing is described by a multiplicative wall-crossing formula. The formula is expressed in terms of graded Lie algebras and involves the study of symplectic structures and automorphisms. The paper also discusses the relationship between these invariants and cluster transformations, as well as their connections to other areas of mathematics, including non-commutative geometry, algebraic geometry, and mathematical physics. The results are supported by various conjectures and examples, and the paper concludes with a discussion of the implications of these results for the study of Calabi-Yau categories and their invariants.