  In this paper, we introduce and study differential graded (DG for short)
polynomial algebras. In brief, a DG polynomial algebra $\mathcal{A}$ is a
connected cochain DG algebra such that its underlying graded algebra
$\mathcal{A}^{\#}$ is a polynomial algebra $\mathbb{k}[x_1,x_2,\cdots, x_n]$
with $|x_i|=1$, for any $i\in \{1,2,\cdots, n\}$.
  We describe all possible differential structures on DG polynomial algebras;
compute their DG automorphism groups; study their isomorphism problems; and
show that they are all homologically smooth and Gorestein DG algebras.
Furthermore, it is proved that the DG polynomial algebra $\mathcal{A}$ is a
Calabi-Yau DG algebra when its differential $\partial_{\mathcal{A}}\neq 0$ and
the trivial DG polynomial algebra $(\mathcal{A}, 0)$ is Calabi-Yau if and only
if $n$ is an odd integer.
