This chapter systematically examines the state of stress at a material point within solid bodies and establishes the fundamental principles governing the spatial variation of stress. The stress tensor, which mathematically characterizes multiaxial stress states in three-dimensional continua, poses considerable conceptual and analytical challenges. Our exposition commences with the elementary one-dimensional stress concept, progressively advancing to the introduction of the Cauchy stress tensor, where rigorous mathematical formulations are meticulously correlated with their physical interpretations through illustrative representations of material stress states. A thorough analytical treatment is presented for essential concepts pertaining to stress states at material points, encompassing the Cauchy stress formula, principal stress analysis, stress tensor invariants, and von Mises equivalent stress. Furthermore, the equations of motion and equilibrium, as well as the symmetry of the stress tensor are rigorously derived through fundamental principles of linear and angular momentum conservation.