Greek symbols are very important in equations: \phi, \pi, \Xi. eLyXer offers a complete set in both upper case: A\Omega and lower case: \alpha\omega. Also the AMS italicized upper case: \varGamma\varOmega.
eLyXer supports the whole set of math symbols in John D. Cook's list: \exists\partial\nabla\geq. It can also render a few more: \propto\times. You also get all symbols from Markus Kuhn's list: \bigodot\amalg.
There are other symbols like arrows: \leftarrow\rightarrow, or geometrical shapes: \circ, \square. eLyXer offers limited support for them. You might also want to use financial symbols in formulae: \yen\euro\$.
Equations look good when items are properly separated. The main separation is the Medium Mathematical Space: x=3.
Note: if you are viewing the non-Unicode version math.html of this page then you are in fact seeing midspaces, which are very similar but not exactly the same: \frac{4}{18}\mathrm{em} for medium mathematical spaces versus \frac{1}{2}\mathrm{en}, where 1\mathrm{em}=2\mathrm{en}. Try out the Unicode version math-unicode.html — and viceversa. You can check out what version this page is in the page title.
The command \raisebox is useful to, surprisingly, raise a little box.
Regular text is shown italicized. Variable: length, \alpha, Speed.
Some font styles can be used in equations. Roman: 1\mathrm{mathrm}. Sans serif: 2\mathsf{mathsf}. Typewriter: 3\mathtt{mathtt}. Bold: 4\mathbf{mathbf}.
Units can be shown with or without a magnitude. Withouth: \unit{km}. With: \unit[57]{km}. With fractional units: \unitfrac[200]{km}{h}. With a fraction before the units: \unit[\nicefrac{3}{2}]{km}, \unit[\frac{7}{16}]{s}.
Some special fonts are supported: \mathscr{mathscr}, \mathcal{MATHCAL}, \mathbb{MATHBB}, \mathfrak{mathfrak}. For those, some single characters are translated to their Unicode equivalents: \mathscr{F}, \mathbb{F}, \mathfrak{F}.
A similar concept is a binomial coefficient: \binom{A+1}{B}. It can be prettily presented:
\dbinom{A}{B+1}.
A symbol can be stacked over another using \stackrel: x\stackrel{R}{\rightarrow}y. Anything can be stacked: d\stackrel{x>3}{\lim}x, \stackrel{head}{heels}.
which should appear as x\rightarrow\infty in italics, and «lim» in plain style. Note that in HTML the limit does not actually appear below the «lim» but to the right. Inlined: \lim_{x\rightarrow\infty}\lyxlock f(x).
Limits are also used in sums:
\sum_{i=1}^{\infty}x,
where the sum’s limits should appear below (i=1) and above (\infty) the \sum. Inlined: \sum_{i=1}^{\infty}x. Also in integrals: \intop_{i=1}^{\infty}x.
Arrays are separated by brackets: \left(a\right)\left[b\right]\left\{ c\right\} \left\langle d\right\rangle \left|e\right|. There are also big brackets: \bigl\langle f\bigr\rangle.
Now it’s time for user-defined commands (sometimes called “macros”).
Definitions can be added as macros
\newcommand{\stupidroot}[2]{\sqrt[#1]{#2}}
{\sqrt[#1]{#2}}
. Then they can be used in formulae: \stupidroot 12. They can accept default parameters
\newcommand{\defaultroot}[2][4][5]{\sqrt[#1]{#2}}
{#1\sqrt{#2}}
. Again, useful in formulae: \defaultroot.
Other definitions from the preamble can be used: \preambleroot{3}{4}.
Definitions on the fly are also possible: \newcommand{\ontheflyroot}[2]{\sqrt[#1]{#2}}\ontheflyroot{7}{8}, and used with different values: \ontheflyroot{a}{b}.