Part
expr[[i]] or Part[expr, i] gives the part of expr.
expr[[-i]] counts from the end.
expr[[i, j, ... ]] or Part[expr, i, j, ... ] is equivalent to expr[[i]] [[j]] ... .
expr[[{ , , ... }]] gives a list of the parts , , ... of expr.
You can make an assignment like t[[i]] = value to modify part of an expression.
When expr is a list, expr[[{ , , ... }]] gives a list of parts. In general, the head of expr is applied to the list of parts.
You can get a nested list of parts from expr[[ , , ... ]]. Each part has one index from each list.
expr[[spec]] can be input as expr spec .
and can be entered as [[ and ]] or \[LeftDoubleBracket] and \[RightDoubleBracket].
expr[[spec]] can be input as or .
See also: First, Last, Position, Take.

Examples
Using InstantCalculators
Here are the InstantCalculators for the Part function. Enter the parameters for your calculation and click Calculate to see the result.
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Entering Commands Directly
You can paste a template for this command via the Text Input button on the Part Function Controller.
This finds the third element from the list using the shorthand notation for Part.
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This pulls out a list of elements.
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The second input resets the third element of the list using the special characters for Part.
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Clear the variable definition.
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