Univariate normal transforms
The general univariate normal distribution with density
$$
f_Y(y) = \frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{(y-\mu)^2}{2\sigma^2}}
$$
is a special case of the multivariate version.
Details
Further, if $Z\sim n(0,1)$, then clearly $X=aZ+\mu \sim n(\mu,\sigma^2)$ where $\sigma^2=a^2$