Extended documentation for mathematical symbols & functions is here.

symbol meaning
@m invoke macro m; followed by space-separated expressions
! prefix “not” operator
a!( ) at the end of a function name, ! indicates that a function modifies its argument(s)
# begin single line comment
#= begin multi-line comment (these are nestable)
=# end multi-line comment
$ bitwise xor operator, string and expression interpolation
% remainder operator
^ exponent operator
& bitwise and
&& short-circuiting boolean and
| bitwise or
|| short-circuiting boolean or
* multiply, or matrix multiply
() the empty tuple
~ bitwise not operator
\ backslash operator
' complex transpose operator AH
a[] array indexing
[,] vertical concatenation
[;] also vertical concatenation
[  ] with space-separated expressions, horizontal concatenation
T{ } parametric type instantiation
{  } construct a cell array (deprecated in 0.4 in favor of Any[])
; statement separator
, separate function arguments or tuple components
? 3-argument conditional operator (conditional ? if_true : if_false)
"" delimit string literals
'' delimit character literals
` ` delimit external process (command) specifications
... splice arguments into a function call or declare a varargs function or type
. access named fields in objects or names inside modules, also prefixes elementwise operators
a:b range a, a+1, a+2, ..., b
a:s:b range a, a+s, a+2s, ..., b
: index an entire dimension (1:end)
:: type annotation, depending on context
:( ) quoted expression
:a symbol a