The theory of tensors and pseudotensors underlies the mathematical framework of modern physics, providing a coordinate-invariant language for describing physical laws and symmetries. In this work, we systematically analyze the transformationproperties of tensors and pseudotensors of various ranks, with particular emphasis on their behavior under spatial and spacetime reflections. The construction and interpretation of the Levi-Civita symbol in two, three, and four dimensionsare discussed in detail, elucidating the essential distinction between true tensors and pseudotensors in terms of orientation and parity. Explicit transformation rules for ordinary tensors and pseudotensors are derived, including the role of the Jacobian determinant and its sign. Through concrete examples—including scalar tripleproducts, cross products, and antisymmetric tensor decompositions—we reveal the fundamental algebraic and geometric features of these mathematical objects. The implications for vector calculus, relativistic field theory, and physical invariants such as chirality and duality are highlighted. Our results provide a unified and rigoroustreatment of the reflection and contraction properties of pseudotensors, with direct relevance to applications in classical mechanics, electromagnetism, and modern theoretical physics.