Abstract: A spin structure on an oriented (Euclidean) vector bundle is a principal spin-bundle that is a non-trivial 2-fold covering of the oriented (orthonormal) frame bundle of $E$, denoted by $P_{SO}(E)$. An (oriented Riemannian) manifold is called spin if its tangent bundle has such a structure. It turns out that the existence of a spin structure has a topological obstruction -- namely, the (vannishing) of the second Stiefel-Whitney class of the manifold. In this talk, we will introduce spin structures and identify the obstruction for its existence in terms of the second Stiefel-Whitney class. Furthermore, some examples will be examined, including showing that for $n$-tori and for compact Riemann surfaces of genus $g$, there are exactly $2^n$ and $2^{2g}$ non-equivalent spin structures, respectively.