what does the triangle in PDE notation mean? what does the triangle sign used in PDE equations represent?

example:
$$u_{tt}- \Delta u =0$$

I took the below example from the Evan's book PDE  p.4 (example 9). The equation is presented as the wave equation. I am not familiar with this notation and it is confusing to me. I know the wave equation in the form of $$u_{tt} - u_{xx} = 0$$ 
Could anybody clarify the notation? Are those two equations the same?
A capital delta $\Delta$ is sometimes used as notation for the Laplacian operator, see e.g. https://en.wikipedia.org/wiki/Laplace_operator. So yes the two equations are the same assuming that the Laplacian is one-dimensional in the first equation.
The upside triangle ($\nabla$) is called the Laplacian. Usually one starts using it as you get PDE's that involve not just $u(x,t)$, but deals with function such as $u(x, y, t)$ or $u(x, y, z, t)$. Hence, with increments of the dimension the Laplacian is generalization of the second partial with respect to the coordinates.

\begin{equation*}
\nabla\phi=\phi_x+\phi_y
\end{equation*}
oR more general,
\begin{equation*}
\nabla\phi=\phi_{x_1}+\dots+\phi_{x_n}
\end{equation*}
where $x_i$ are nothing more than the coordinates that your applying the second partials to, namely the Laplacian operator.