For the mathematician and linquistist 
ε 
the empty string 
x 
the symbol x 
α β 
The RE α followed by the RE β 
α  β 
Either α or β 
α^{*} 
Zero or more sequences of α 
(α) 
α grouped 
Examples include 
(01)*0 
All even binary numbers 
1*01*0(01)* 
All binary numbers containing at least two 0's 
(01)*111(01)* 
All binary numbers that contain the sequence "111" somewhere in the number 
For the Unix guru using grep, ed, sed, ... 
x 
Matches the nonspecial character.
The characters '?', '\',
'.', '[', ']', '^',
'$', '*', '(', and ')'.
are special

[aeiou] 
Matches characters inside the brackets. 
[09AF] 
Matches a range of characters. 
. 
Matches any character 
PATTERN* 
Matches a PATTERN occuring zero or more times. 
PATTERN+ 
Matches a PATTERN occuring one or more times. 
PATTERN? 
Matches a PATTERN occuring zero or one time. 
For the Perl programmer 