The Wolfram Language's uniform representation of vectors and matrices as lists automatically extends to tensors of any rank, allowing the Wolfram Language's powerful list manipulation functions immediately to be applied to tensors, both numerical and symbolic.

Table — construct a tensor of any rank from an expression

Array — construct a tensor from a function: Array[f,dims]

SparseArray — specify a tensor in a sparse position⟶value form

Dimensions — the dimensions of a tensor

ArrayDepth — the rank of a tensor

ArrayQ — test whether an object is a tensor of a given rank

MatrixForm — display a tensor of any rank

KroneckerDelta — identity tensor

LeviCivitaTensor — totally antisymmetric tensor

Band — specify banded structure in a sparse array

Transpose — transpose to rearrange indices in any way

Dot (.) — dot product

Inner — generalized inner product

Outer — generalized outer product

Tr — generalized trace

ArrayReduce — reduce any tensor indices with a function (e.g. Total)

Flatten — flatten out any sequence of levels

ArrayFlatten  ▪  Partition  ▪  PadLeft  ▪  PadRight