Corollary 35.2:

The homology groups of the spheres $S^n$ ($n\geq 1$) are given by

$$H_m(S^n) = \left\{\begin{array}{lll} 0 & & \mbox{ if } m \neq 0,\; m \neq n \\ \mathbb{Z} & & \mbox{ if } m = 0,\; m = n \\ \end{array} \right.$$