In mathematics, there is generally no meaningful difference among parentheses, square brackets, and curly braces (see right), and so they are used interchangeably, but often in combination to ease the reader’s task of identifying which open-brace matches with which close-brace. In Mathematica™, however, these three types of braces have fundamentally different meanings, and it is critical to ensure that you are using the correct brace for a particular function.
Parentheses are used in Mathematica™ to group elements of expressions together in order to specify a non-standard order of operations, and can be nested as deeply as you like. This is what we normally think of as the standard behavior of braces.
Square brackets are used to set off function arguments.
Curly braces are used to group elements of a list together. There will be a complete separate tutorial concerning lists.
Double Square Brackets
Double Square Brackets are used to select specific elements from a list.