In this manuscript, we continue to study the hypersoft topological space (for short, HSTS) by presenting hypersoft (HS) separation axioms, called HS T i-spaces for i = 0, 1, 2, 3, 4. The notions of HS regular and HS normal spaces are explained in detail. We discuss the connections between them and present numerous examples to help clarify the interconnections between the different types of these spaces. We point out that HS T i-axioms imply HS T i−1 for i = 1, 2, 3, and with the help of an example we show that HS T 4-space need not be HS T 3-space. We also clarify that the property that an HS space being HS T i-spaces (i = 0, 1, 2, 3) is HS hereditary. Finally, we provide a diagram to illustrate the relationships between our proposed axioms.