Defining Custom Notation
The Wolfram Language's unified symbolic architecture allows arbitrary extensibility in the output and input of notation.
Local Interpretations »
Interpretation — specify any interpretation for any expression
Iconize — convert any expression to display in an iconized form
DynamicSetting — display as a control that returns its setting when evaluated
Keyboard Macros
InputAutoReplacements — automatic replacements for sequences of input characters
InputAliases — aliases for arbitrary expressions, input with 
Low-Level Definitions
MakeBoxes — settable low-level translator from expression to display boxes
MakeExpression — settable low-level translator from boxes to evaluatable expressions
Format — settable low-level translator from various forms to evaluatable expressions
ToBoxes — generate the display boxes of an evaluated expression
StripBoxes — strip a box expression of whitespace and styling
TagBox ▪ TemplateBox ▪ InterpretationBox ▪ ...
Built-in Symbolic Notational Forms »
CirclePlus(⊕) ▪ Subscript ▪ Overscript ▪ OverBar ▪ Infix ▪ ...