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Structural Operations on Expressions
Mathematica's unified symbolic architecture immediately allows it to perform structural transformations not only on objects like lists, but also on general symbolic expressions that can represent concrete or abstract data of any kind.
Flatten flatten out nested functions (associativity)
Thread thread a function over lists or other constructs
Sort sort elements of an expression (commutativity)
    
FlattenAt flatten particular elements
Distribute apply distributivity to nested functions
Reverse  ▪ Transpose  ▪ Outer
    
Join join expressions together
Append  ▪ Prepend  ▪ Take  ▪ Drop
    
Part([[...]])  ▪ ReplacePart  ▪ MapAt  ▪ ...
Head-Related Operations
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