It‘s a very elegant summary of regular expression from The AWK Programming Language.

1. The regular expression metacharacters are:  

 \ ^ $ . [ ] | ( ) * + ?

2. A basic regular expression is one of the following:

• a nonmetacharacter, such as A, that matches itself.
• an escape sequence that matches a special symbol: \t matches a tab.
• a quoted metacharacter, such as \*, that matches the metaqcharacter literally.
• ^, which matches the beginning of a string.
• $, which matches the end of a string.
• ., which matches any single character.
• a character class: [ABC] matches any of the characters A, B, or C. Character classes may include abbreviations: [A-Za-z] matches any single letter.
• a complemented character class: [^0-9] matches any character except a digit.

3. These operators combine regular expressions into larger ones:

• alternation: A | B matches A or B.
• concatenation: AB matches A immediately followed by B.
• closure: A* matches zero or more A‘s.
• positive closure: A+ matches one or more A‘s.
• zero or one: A? matches the null string or A.
• parentheses: (r) matches the same strings as r does.

Regular Expression