  We study the rigidity questions and the Albanese Variety for Complex
Parallelizable Manifolds. Both are related to the study of the cohomology group
$H^1(X,\mathcal O)$. In particular we show that a compact complex
parallelizable manifold is rigid iff $b_1(X)=0$ iff Alb$(X)=\{e\}$ iff
$H^1(X,\mathcal O)=0$.
