Homology of Klein bottle

Statement
The homology of the Klein bottle $$K$$ is given by:

$$H_0(K) = \mathbb{Z}$$

and:

$$H_1(K) = \mathbb{Z} \oplus \mathbb{Z}/2\mathbb{Z}$$

All other homology groups are 0.

Related invariants
These are all invariants that can be computed in terms of the homology groups.