The feature that makes LaTeX the right edition tool for scientific documents is the ability to render complex mathematical expressions. This article explains the basic commands to display equations.
Contents 
Basic equations in LaTeX can be easily "programmed", for example:
The well known Pythagorean theorem \(x^2 + y^2 = z^2\) was proved to be invalid for other exponents. Meaning the next equation has no integer solutions: \[ x^n + y^n = z^n \]
As you see, the way the equations are displayed depends on the delimiter, in this case \[ \]
and \( \)
.
LaTeX allows two writing modes for mathematical expressions: the inline mode and the display mode. The first one is used to write formulas that are part of a text. The second one is used to write expressions that are not part of a text or paragraph, and are therefore put on separate lines.
Let's see an example of the inline mode:
In physics, the massenergy equivalence is stated
by the equation $E=mc^2$, discovered in 1905 by Albert Einstein.
To put your equations in inline mode use one of these delimiters: \( \)
, $ $
or \begin{math} \end{math}
. They all work and the choice is a matter of taste.
The displayed mode has two versions: numbered and unnumbered.
The massenergy equivalence is described by the famous equation $$E=mc^2$$ discovered in 1905 by Albert Einstein. In natural units ($c$ = 1), the formula expresses the identity \begin{equation} E=mc^2 \end{equation}
To print your equations in display mode use one of these delimiters: \[ \]
, $$ $$
, \begin{displaymath} \end{displaymath}
or \begin{equation} \end{equation}
Important Note: equation*
environment is provided by an external package, consult the amsmath article.
Below is a table with some common maths symbols. For a more complete list see the List of Greek letters and math symbols:
description  code  examples 

Greek letters  \alpha \beta \gamma \rho \sigma \delta \epsilon 
$$ \alpha \ \beta \ \gamma \ \rho \ \sigma \ \delta \ \epsilon $$ 
Binary operators  \times \otimes \oplus \cup \cap 

Relation operators  < > \subset \supset \subseteq \supseteq 

Others  \int \oint \sum \prod 
Different classes of mathematical symbols are characterized by different formatting (for example, variables are italicized, but operators are not) and different spacing.
The mathematics mode in LaTeX is very flexible and powerful, there is much more that can be done with it: