Let \(\mathfrak{g}\) be the complexification of the Lie algebra of a real reductive group \(G\). Assume that \((\mathfrak{g},\mathfrak{k})\) is a symmetric pair such that Spin\(_{ad}\) is a primary representation. Put differently, if we denote by \(\mathfrak{t}\) Cartan subalgebra of \(\mathfrak{k}\), then we have an equality of Weyl groups \((W_{\mathfrak{k},t} = W_{\mathfrak{g},t}\). Main goal of this dissertation is to show some new results in the relative Weil and Clifford algebra, analogous to famous results in the absolute case. First result will be an explicit formula for the transgression in the relative Weil algebra \(W(\mathfrak{g},\mathfrak{k}) = (S (\mathfrak{g}) \otimes \wedge \mathfrak{p})^{\mathfrak{k}} \). Further, the transgression theorem will be proved in this case; this theorem gives us the image and the kernel of the transgression map. For a symmetric pair \((\mathfrak{g},\mathfrak{k})\) as before let \(\mathfrak{g} = \mathfrak{k} \oplus \mathfrak{p}\) be the Cartan decomposition. Let \(\mathfrak{h}\) be the fundamental Cartan subalgebra, so \(\mathfrak{h} = t \oplus \mathfrak{a}\), where \(\mathfrak{a} = \mathfrak{h} \cap \mathfrak{p}\). Another goal of this dissertation is to introduce Harish-Chandra map on the Clifford algebra \(C(\mathfrak{p})\) as a projection to \(C(\mathfrak{a})\) for a choice of positive \((\mathfrak{g},\mathfrak{t})\) roots. It will be shown that the restriction of the Harish-Chandra map to \(\mathfrak{k}\)-invariants in \(C(\mathfrak{p})\) is an algebra isomorphism \(C(\mathfrak{p})^{\mathfrak{k}} \rightarrow C(\mathfrak{a})\).