In geometric approach the starting point of the formulation of quantum theory is the cone of states. I'll explain this approach, the algebraic approach , the textbook formulation of quantum mechanics and the relations between these approaches. I'll show how the formulas for probabilities can be obtained from basic principles. I'll talk in more detail about the case when the cone of states is homogeneous and about the relation of homogeneous cones to Jordan algebras and homogeneous complex domains.