Alain Connes developed Cyclic homology as a non-commutative analogue of de Rham cohomology, which can be viewed as a Lie analogue of algebraic $K$-theory. In this talk, we will begin by defining chain complexes, followed by an introduction to Hochschild homology and various perspectives on Cyclic homology. A key focus will be on the theorem stating that if $k$ contains $\mathbb{Q}$, the $k$-algebra $A$ is commutative, and the $A$-bimodule $M$ is symmetric, then the Hochschild complex $C_*(A, M)$ splits into a sum of sub-complexes $C_*^{(i)}$, $i \geq 0$, and the bicomplex $\mathcal{B}(A)$ similarly decomposes into sub-complexes $\mathcal{B}(A)^{(i)}$, $i \geq 0$. We will also discuss the Eulerian idempotents, the Eulerian decomposition of $S_n$, and Cyclic descents, which facilitate a $\lambda$-decomposition of Hochschild and Cyclic homology.