Flatten out lists at all levels:

Flatten only at level 1:

Flatten levels 2 and 3 of an array of depth 3 into the first level of the resulting matrix:

Flatten a sparse array:

Flatten works with any head:

Flatten all levels with respect to g:

Flatten all levels with respect to f:

Here is a matrix:

Flatten an array of blocks with the shape of u into a single matrix:

Flatten into a single matrix, effectively using the transpose of the blocks:

Join lists and individual elements:

Unravel a matrix:

Make a flattened list of rules:

Do a "transpose" on a ragged array:

Contract three levels of arrays in a single Dot operation by flattening them first:

Obtain the same result by explicit contraction of three pairs of levels:

Flatten acts as an inverse of Partition:

ArrayReshape acts as an inverse for Flatten on rectangular arrays:

For a rectangular array a, ArrayFlatten[a,r] is equivalent to Flatten[a,{{1,r+1},{2,r+2},…,{r,2r}}]:

Flatten effectively arranges elements in the lexicographic order of their indices:

For a permutation p with inverse , Flatten[a,List/@p^-1]==Transpose[a,p]:

A random permutation:

Get its inverse:

Peel off successive layers of Framed: