How to | Use Brackets and Braces Correctly
Mathematica's rich syntax uses different kinds of brackets and braces; familiarity with these aspects lets you read and program efficiently in Mathematica.
Parentheses ( ), braces { }, and square brackets [ ] all have different meanings in Mathematica. The first two are sometimes called round brackets and curly brackets.
You use parentheses 
in Mathematica for grouping expressions and to determine the precedence of operations:
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A list in Mathematica is represented by braces 
and is a collection of items referred to as elements.
Create a list of the first five positive integers:
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Anything in Mathematica can be used in lists, including numbers, variables, typeset mathematical expressions, and strings:
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Lists can contain other lists to create nested lists:
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Square brackets are used in Mathematica to enclose the arguments of functions.
The functions Range, Sin, and N are used here with square brackets enclosing their arguments:
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Mathematica uses double square brackets as the short form 
for the Part function, which is used to get parts of lists:
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The various bracketing constructions can be used together.
Plot a function, with the range of the plot specified in a list:
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The ability to use functions and lists together is seamlessly integrated in Mathematica. Plot two functions together—the pair of functions is in a list:
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All bracketing characters must be balanced for Mathematica to evaluate an expression. When a bracketing character is unbalanced, the Mathematica front end colors it purple:
Attempting to evaluate the expression produces an error:
For more information on balancing brackets and braces, see How to: Balance Brackets and Braces.
