Dots, horizontal or vertical

Ellipses are the three dots (usually three) indicating that a pattern continues.

\begin{array}{cccc}
  a_{0,0}    &a_{0,1}   &a_{0,2} &\ldots \\
  a_{1,0}    &\ddots                     \\
  \vdots
\end{array}

LaTeX provides these.

\cdots

Horizontal ellipsis with the dots raised to the center of the line, as in ⋯. Used as: \( a_0\cdot a_1\cdots a_{n-1} \).

\ddots

Diagonal ellipsis, ⋱. See the above array example for a usage.

\ldots

Ellipsis on the baseline, …. Used as: \( x_0,\ldots x_{n-1} \). Another example is the above array example. A synonym is \mathellipsis. A synonym from the amsmath package is \hdots.

You can also use this command outside of mathematical text, as in The gears, brakes, \ldots{} are all broken. (In a paragraph mode or LR mode a synonym for \ldots is \dots.)

\vdots

Vertical ellipsis, ⋮. See the above array example for a usage.

The amsmath package has the command \dots to semantically mark up ellipses. This example produces two different-looking outputs for the first two uses of the \dots command.

\usepackage{amsmath}  % in preamble
  ...
Suppose that \( p_0, p_1, \dots, p_{n-1} \) lists all of the primes.
Observe that \( p_0\cdot p_1 \dots \cdot p_{n-1} +1 \) is not a
  multiple of any \( p_i \).
Conclusion: there are infinitely many primes \( p_0, p_1, \dotsc \).

In the first line LaTeX looks to the comma following \dots to determine that it should output an ellipsis on the baseline. The second line has a \cdot following \dots so LaTeX outputs an ellipsis that is on the math axis, vertically centered. However, the third usage has no follow-on character so you have to tell LaTeX what to do. You can use one of the commands: \dotsc if you need the ellipsis appropriate for a comma following, \dotsb if you need the ellipses that fits when the dots are followed by a binary operator or relation symbol, \dotsi for dots with integrals, or \dotso for others.