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LaTeX for beginners

LaTeX is widely used by mathematicians, scientists and engineers to write equations. Although the notation may look unfamiliar at first, it is based on a few simple ideas. This page introduces commands, superscripts, subscripts and groups, explains how to type special characters, and covers fractions, sums, integrals, matrices and tables. It ends with a complete LaTeX document showing how to include equations from fxEditor in a paper or thesis.

You do not need to learn LaTeX to use fxEditor — the toolbar writes it for you — but knowing how it works makes you much faster. Type into the box under the equation below and watch it change, and click any example on this page to open it here and try it yourself.

The basics: letters, numbers and commands

In LaTeX maths, what you type is mostly what you get. Letters become variables, set in italic; numbers and the symbols on your keyboard (+ - = < > ( ) [ ] / | ! ' :) stand for themselves. Everything else is a command: a backslash followed by a name, such as \alpha, \infty or \times.

Spaces you type are ignored in maths — LaTeX spaces an equation itself, by what each piece is (a + gets more room than a letter). A space does matter in one place: it ends a command's name, so \alpha x is α times x, while \alphax is a command called alphax, which does not exist.

a+b = c

a + b = c

Letters are variables, in italic. Spaces make no difference.

2\pi r \times \alpha \leq \infty

2 π r \times α \leq \infty

Commands start with a backslash: Greek letters, operators and symbols.

\sin x + \log y \neq sinx

\sin x + \log y \neq s i n x

Functions such as \sin and \log are commands too. Without the backslash, sinx is read as four variables multiplied together.

a\,b \; c \quad d \qquad e

a b c d e

If you do want space: \, thin, \; thick, \quad and \qquad wide.

In a LaTeX document, maths in a line of text goes between $ ... $ (or $ ... $), and an equation on a line of its own between \[ ... \]. In fxEditor you type only what goes inside.

Superscripts and subscripts: ^ and _

The caret ^ raises what follows it into a superscript (a power), and the underscore _ lowers it into a subscript (an index). The rule that catches out every beginner: each applies to the one next thing only — a single character, a single command, or a group in braces.

x^2 \quad x_i

x^{2} x_{i}

One character: no braces needed.

x^10

x^{1} 0

Wrong: only the 1 is raised, and the 0 sits on the line.

x^{10} \quad a_{n+1}

x^{10} a_{n + 1}

Right: braces make 10 and n+1 one thing.

x_i^2 = x^2_i

x_{i}^{2} = x^{2}_{i}

Both at once, in either order: they stack.

e^{-x^2/2}

e^{- x^{2} / 2}

A superscript can hold anything, even another superscript.

x^{a^b} \quad {x^a}^b

x^{a^{b}} {x^{a}}^{b}

Braces say which is which: x to the a^b, or x^a to the b.

T_{\text{max}} \quad a_{i,j} \quad \alpha_\beta

T_{max} a_{i, j} α_{β}

A command counts as one thing, so \alpha_\beta needs no braces. \text makes a word upright.

{}^{14}_{6}\mathrm{C}

^{14}_{6} C

Scripts before a symbol: attach them to an empty group, {}.

Writing x^^2 or x__i is an error: a symbol can have only one of each. To add a prime as well, f'(x) and f''(x) just work.

Groups: { and }

Braces are LaTeX's way of saying “treat all of this as one thing”. They are never printed. You have already seen them hold a superscript together; they also hold together the arguments of a command. \frac takes two — a numerator and a denominator — each in its own pair of braces; \sqrt takes one.

\frac{a+b}{2}

\frac{a + b}{2}

\frac{top}{bottom}: two groups, two arguments.

\frac12 \quad \frac a b

\frac{1}{2} \frac{a}{b}

As with ^, an argument of one character needs no braces — but braces are clearer.

\sqrt{x^2+y^2}

\sqrt{x^{2} + y^{2}}

Groups inside groups: the square root of a sum of squares.

(a+b) \quad \{a+b\}

(a + b) {a + b}

To print braces, escape them: \{ and \}. Round brackets need nothing.

Every { needs its }. When an equation goes wrong, a missing or extra brace is the first thing to look for.

Special characters, and how to escape them

Ten characters mean something to LaTeX, so typing one does not print it. To print most of them, put a backslash in front — that is called escaping it.

Character	What it does	To print it
`\`	starts a command	`\backslash` in maths, `\textbackslash` in text
`{ }`	make a group	`\{` and `\}`
`^`	superscript	`\hat{x}` for a hat on x, `\wedge` for ∧, `\^{}` in text
`_`	subscript	`\_`
`&`	separates the columns of a matrix or table	`\&`
`%`	starts a comment — the rest of the line is ignored	`\%`
`$`	starts and ends maths in a document	`\$`
`#`	a parameter, in a command you define	`\#`
`~`	a space the line will not break at	`\sim` in maths, `\textasciitilde` in text

\{ \} \_ \& \% \$ \#

{}_& % $ #

Seven of them, escaped.

\text{Profit: } 15\% \text{ of } \$200

Profit: 15 % of $ 200

Forget the backslash before % and the rest of the line vanishes as a comment.

\{\, x \mid x > 0 \,\}

{x ∣ x > 0}

A set: escaped braces, and \mid for the bar.

Note that \\ is not an escaped backslash: it is the command that starts a new line, or a new row of a matrix or table.

Fractions, roots and brackets

Brackets typed as ( ) or [ ] stay one size. Put \left and \right in front of them and they grow to fit what is between them. The two must always be used as a pair; \left. or \right. is an invisible bracket, for when you want only one side.

\frac{1}{1+\frac{1}{x}}

\frac{1}{1 + \frac{1}{x}}

A fraction in a fraction.

\sqrt{2} \quad \sqrt[3]{x} \quad \sqrt[n]{1+x}

\sqrt{2} \sqrt[3]{x} \sqrt[n]{1 + x}

The optional argument, in square brackets, is the root's index.

(\frac{a}{b}) \quad \left( \frac{a}{b} \right)

(\frac{a}{b}) (\frac{a}{b})

Plain brackets, then brackets that fit.

\left[ \sum_{k=1}^{n} x_k \right]^2

{[\sum_{k = 1}^{n} x_{k}]}^{2}

Square brackets that grow, then squared.

\left. \frac{df}{dx} \right|_{x=0}

{\frac{d f}{d x} |}_{x = 0}

“Evaluated at”: an invisible left bracket and a bar on the right.

\binom{n}{k} = \frac{n!}{k!\,(n-k)!}

(\binom{n}{k}) = \frac{n!}{k! (n - k)!}

A binomial coefficient.

Sums, products, integrals and limits

The big operators — \sum, \prod, \int and the rest — take their limits with the same _ and ^ as anything else. Where the limits go depends on the operator and on the space: on an equation of its own, a sum's limits sit above and below it; in a line of text, beside it, so as not to push the lines apart. An integral's limits always go beside it unless you ask, with \limits.

\sum_{k=1}^{n} k^2 = \frac{n(n+1)(2n+1)}{6}

\sum_{k = 1}^{n} k^{2} = \frac{n (n + 1) (2 n + 1)}{6}

A sum, with its limits above and below.

\textstyle \sum_{k=1}^{n} k^2

\sum_{k = 1}^{n} k^{2}

The same sum as it is set in a line of text.

\prod_{i=1}^{n} x_i

\prod_{i = 1}^{n} x_{i}

A product.

\int_0^\infty e^{-x}\,dx = 1

\int_{0}^{\infty} e^{- x} d x = 1

An integral. \, puts the small space LaTeX does not add before dx.

\int\limits_a^b f(x)\,dx

\int_{a}^{b} f (x) d x

\limits puts an integral's limits above and below.

\iint_D f\,dA \quad \iiint_V \rho\,dV \quad \oint_C \mathbf{F}\cdot d\mathbf{r}

\iint_{D} f d A ∭_{V} ρ d V \oint_{C} 𝐅 \cdot d 𝐫

Double, triple and contour integrals.

\lim_{x \to 0} \frac{\sin x}{x} = 1

lim_{x \to 0} \frac{\sin x}{x} = 1

\lim: the condition goes below, in a subscript.

\sum_{\substack{0 < i < m \\ 0 < j < n}} P(i,j)

\sum_{\begin{array}{c} 0 < i < m \\ 0 < j < n \end{array}} P (i, j)

A limit of more than one line: \substack, with \\ between the lines.

Text and fonts in an equation

Words typed straight into maths come out as italic variables, run together. Put them in \text{...} instead: it is set as ordinary text, and spaces inside it count. For a function LaTeX has no command for, use \operatorname, which spaces it as it does \sin.

x = 1 if y > 0

x = 1 i f y > 0

Wrong: “if” is read as i times f.

x = 1 \text{ if } y > 0

x = 1 if y > 0

Right: the spaces inside \text are kept.

\operatorname{sgn}(x) \quad \operatorname{Var}(X)

sgn (x) Var (X)

Functions of your own.

\mathbf{v} \quad \mathbb{R} \quad \mathcal{L} \quad \mathrm{d}x

𝐯 ℝ ℒ d x

Bold, blackboard bold, calligraphic and upright.

Matrices

A matrix is written row by row. & separates the entries in a row, and \\ ends the row. The name of the environment chooses the brackets around it; the entries are always centred.

\begin{matrix} a & b \\ c & d \end{matrix}

\begin{array}{c} a & b \\ c & d \end{array}

matrix: no brackets.

\begin{pmatrix} a & b \\ c & d \end{pmatrix}

(\begin{array}{c} a & b \\ c & d \end{array})

pmatrix: parentheses.

\begin{bmatrix} a & b \\ c & d \end{bmatrix}

[\begin{array}{c} a & b \\ c & d \end{array}]

bmatrix: square brackets.

\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc

| \begin{array}{c} a & b \\ c & d \end{array} | = a d - b c

vmatrix: bars, for a determinant. Vmatrix gives double bars and Bmatrix braces.

I_n = \begin{pmatrix} 1 & 0 & \cdots & 0 \\ 0 & 1 & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & 1 \end{pmatrix}

I_{n} = (\begin{array}{c} 1 & 0 & \dots & 0 \\ 0 & 1 & \dots & 0 \\ ⋮ & ⋮ & ⋱ & ⋮ \\ 0 & 0 & \dots & 1 \end{array})

Dots: \cdots across, \vdots down, \ddots diagonally.

\mathbf{x} = \begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix}

𝐱 = (\begin{array}{c} x_{1} \\ x_{2} \\ x_{3} \end{array})

A column vector: one entry per row.

Arrays and tables: for maths, and for text

When you need more than a matrix gives you — columns aligned left or right, lines between them — use array or tabular. The two are written the same way, and look alike. The difference is what goes in the cells:

array is for maths. Every cell is maths: x^2 is x squared, letters are italic variables. Use it inside an equation.

tabular is for text. Every cell is text, as in a sentence: words keep their spaces and are upright, and x^2 is not a power. To put maths in a cell, wrap it in $...$ . In a document, a table of words or data is a tabular.

\begin{array}{cc} x^2 & area of square \end{array}

\begin{array}{cc} x^{2} & a r e a o f s q u a r e \end{array}

array: the words become italic letters, with their spaces lost.

\begin{tabular}{cc} x^2 & area of square \end{tabular}

\begin{array}{cc} x^2 & area of square \end{array}

tabular: the words are right, but x^2 is printed as typed.

\begin{tabular}{cc} $x^2$ & area of square \end{tabular}

\begin{array}{cc} x^{2} & area of square \end{array}

Right: a text table, with $...$ round the maths.

Both begin with a column specification in braces, one letter for each column, saying how it is aligned:

In the specification	Gives
`l`, `c`, `r`	a column aligned left, centred, or right
`p{3cm}`	a column of text 3 cm wide, which wraps onto more lines (in a document)
`\|`	a vertical line between the columns either side of it
`\|\|`	a double vertical line

\begin{array}{lcr} 1 & 1 & 1 \\ 100 & 100 & 100 \\ 10 & 10 & 10 \end{array}

\begin{array}{lcr} 1 & 1 & 1 \\ 100 & 100 & 100 \\ 10 & 10 & 10 \end{array}

{lcr}: the first column left-aligned, the second centred, the third right.

\begin{array}{rl} 3x + 2 & = 11 \\ 3x & = 9 \\ x & = 3 \end{array}

\begin{aligned} 3 x + 2 & = 11 \\ 3 x & = 9 \\ x & = 3 \end{aligned}

{rl}: equations lined up on their equals signs.

\left( \begin{array}{cc|c} 1 & 2 & 3 \\ 4 & 5 & 6 \end{array} \right)

(\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \end{array})

An augmented matrix: an array with a line, in brackets.

Aligning equations, and cases

For working that runs over several lines, aligned is simpler than an array: put & just before the sign to line up on, and \\ at the end of each line. cases is the brace for a function defined piece by piece; each line has a value, then &, then its condition.

\begin{aligned} (a+b)^2 &= (a+b)(a+b) \\ &= a^2 + 2ab + b^2 \end{aligned}

{(a + b)}^{2}

= (a + b) (a + b)

= a^{2} + 2 a b + b^{2}

aligned: the lines line up at each &=.

|x| = \begin{cases} x & \text{if } x \geq 0 \\ -x & \text{if } x < 0 \end{cases}

| x | = {\begin{cases} x & if x \geq 0 \\ - x & if x < 0 \end{cases}

cases, with \text for the words.

Borders and lines

Vertical lines go in the column specification, as |. Horizontal lines go between the rows, as \hline: one at the start draws a line along the top, one after a \\ draws a line under that row. \hline\hline draws a double line. The same works in array and tabular.

\begin{array}{|c|c|} \hline a & b \\ \hline c & d \\ \hline \end{array}

\begin{array}{cc} a & b \\ c & d \end{array}

A border round every cell: | between and around the columns, \hline above, between and below the rows.

\begin{array}{|cc|} \hline a & b \\ c & d \\ \hline \end{array}

\begin{array}{cc} a & b \\ c & d \end{array}

A box round the outside only.

\begin{array}{c|cc} \times & 1 & 2 \\ \hline 1 & 1 & 2 \\ 2 & 2 & 4 \end{array}

\begin{array}{ccc} \times & 1 & 2 \\ 1 & 1 & 2 \\ 2 & 2 & 4 \end{array}

A heading row and column, divided from the rest.

\begin{array}{c||c} a & b \\ \hline\hline c & d \end{array}

\begin{array}{cc} a & b \\ c & d \end{array}

Double lines: || and \hline\hline.

\begin{tabular}{|l|r|} \hline Item & Cost \\ \hline Tea & 2.50 \\ Cake & 3.00 \\ \hline Total & 5.50 \\ \hline \end{tabular}

\begin{array}{lr} Item & Cost \\ Tea & 2.50 \\ Cake & 3.00 \\ Total & 5.50 \end{array}

A text table: words left-aligned, numbers right-aligned so their decimal points line up.

Changing the thickness of the lines

Every line in an array or table is \arrayrulewidth thick — 0.4 pt unless you change it. Set it with \setlength before the table, and every line in it, across and down, is drawn that thick:

\setlength{\arrayrulewidth}{1.5pt} \begin{array}{|c|c|} \hline a & b \\ \hline c & d \\ \hline \end{array}

\begin{array}{cc} a & b \\ c & d \end{array}

Lines 1.5 pt thick.

\setlength{\arrayrulewidth}{3pt} \begin{tabular}{|c|} \hline Thick \\ \hline \end{tabular}

\begin{array}{c} Thick \end{array}

Lines 3 pt thick.

Using your equations in a LaTeX document

Everything fxEditor makes is LaTeX, so it can go straight into a document. Here is a complete one, using most of what is on this page. Copy the LaTeX from fxEditor's box and paste it between \[ and \] for an equation on its own line, or between $ and $ in the middle of a sentence.

\documentclass{article}

\usepackage{amsmath}    % matrices, cases, aligned, \text, \operatorname, \binom, \iint
\usepackage{amssymb}    % extra symbols, and \mathbb for R, N, Z ...
\usepackage{xcolor}     % colours: \textcolor{red}{x}
\usepackage{fxpicture}  % pictures from fxEditor's picture editor (loads pict2e)

\begin{document}

\section*{A short example}

The roots of $ax^2 + bx + c = 0$ are
\[
  x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
\]

The sum of the first $n$ squares is
\[
  \sum_{k=1}^{n} k^2 = \frac{n(n+1)(2n+1)}{6},
\]
and the area under a bell curve is
\[
  \int_{-\infty}^{\infty} e^{-x^2}\,dx = \sqrt{\pi}.
\]

A rotation through an angle $\theta$, and the absolute value:
\[
  R = \begin{pmatrix} \cos\theta & -\sin\theta \\
                      \sin\theta &  \cos\theta \end{pmatrix},
  \qquad
  |x| = \begin{cases} x  & \text{if } x \geq 0 \\
                      -x & \text{if } x < 0 \end{cases}
\]

\begin{center}
\setlength{\arrayrulewidth}{0.8pt}
\begin{tabular}{|l|r|}
  \hline
  Item & Cost (\$) \\
  \hline
  Tea  & 2.50 \\
  Cake & 3.00 \\
  \hline
\end{tabular}
\end{center}

A right-angled triangle, drawn with fxEditor's picture editor:
\[
  \begin{picture}(58,54)(-11,-12)
    \polygon(0,0)(45,0)(0,40)
    \polyline(4,0)(4,4)(0,4)
    \put(-9,17){$a$}
    \put(20,-10){$b$}
    {\linestyle{dashed}\Line(0,0)(22.5,20)}
  \end{picture}
\]

\end{document}

The packages

Package	Needed for
`amsmath`	Almost every document with maths in it. The matrix environments, `cases`, `aligned`, `\text`, `\operatorname`, `\binom`, `\substack`, `\boxed`, `\iint` and more.
`amssymb`	Extra symbols, and `\mathbb` (ℝ, ℕ, ℤ).
`xcolor`	Coloured maths. In a document use `\textcolor{red}{x}`, or `{\color{red} x}` with the colour in a group of its own.
`fxpicture`	Pictures from fxEditor's picture editor. It loads `pict2e` and adds dashed and dotted lines. It is not in TeX distributions yet: download fxpicture.zip and put `fxpicture.sty` beside your `.tex` file. A picture with only solid lines needs just `pict2e`.
`mhchem`, `chemfig`, `physics`	Only if you use those packages in fxEditor — `\ce{...}`, `\chemfig{...}`, `\dv`, `\ket` and the like.

Compiling it: pdfLaTeX or XeLaTeX

A .tex file is a set of instructions; a TeX engine reads them and writes the PDF. You need a TeX distribution installed — TeX Live on Linux and Windows, MacTeX on a Mac, or MiKTeX on Windows — or an online editor such as Overleaf, which needs nothing installed. Save the document above as example.tex, with fxpicture.sty beside it, and run:

pdflatex example.tex

This writes example.pdf. pdfLaTeX is the usual choice, and the right one for this document: it is fast, and every journal accepts it. Use XeLaTeX (or LuaLaTeX) instead when the document needs fonts installed on your computer — with the fontspec or unicode-math packages — or is written in a language pdfLaTeX struggles with, such as Arabic, Chinese or Hindi:

xelatex example.tex

Both read the same document, and fxpicture works in both. If a document has cross-references (\label and \ref) or a table of contents, run the command twice, so the second run can fill in what the first found. latexmk -pdf example.tex (or latexmk -xelatex) runs it as many times as needed for you. In Overleaf, choose the engine under Menu → Compiler.

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