Reformatting a table to save vertical space
mat = Array[Symbol["a" <> ToString@# <> ToString@#2] &, {6, 3}];
TeXForm @ MatrixForm @ mat
$\left( \begin{array}{ccc} \text{a11} & \text{a12} & \text{a13} \\ \text{a21} & \text{a22} & \text{a23} \\ \text{a31} & \text{a32} & \text{a33} \\ \text{a41} & \text{a42} & \text{a43} \\ \text{a51} & \text{a52} & \text{a53} \\ \text{a61} & \text{a62} & \text{a63} \\ \end{array} \right)$
mat2 = Join[## & @@ Partition[mat, 2], 2];
mat2 // MatrixForm // TeXForm
$\left( \begin{array}{ccccccccc} \text{a11} & \text{a12} & \text{a13} & \text{a31} & \text{a32} & \text{a33} & \text{a51} & \text{a52} & \text{a53} \\ \text{a21} & \text{a22} & \text{a23} & \text{a41} & \text{a42} & \text{a43} & \text{a61} & \text{a62} & \text{a63} \\ \end{array} \right)$
Also:
mat3 = Join @@@ Transpose[Partition[mat, 2]];
mat4 = Join @@@ Multicolumn[mat, {2, Automatic}][[1]]
mat4 == mat3 == mat2
True
Another more complex method :-)
$$\left( \begin{array}{ccc} \text{a11} & \text{a12} & \text{a13} \\ \text{a21} & \text{a22} & \text{a23} \\ \text{a31} & \text{a32} & \text{a33} \\ \text{a41} & \text{a42} & \text{a43} \\ \text{a51} & \text{a52} & \text{a53} \\ \text{a61} & \text{a62} & \text{a63} \\ \end{array} \right)$$
mat={{a11, a12, a13}, {a21, a22, a23}, {a31, a32, a33}, {a41, a42,
a43}, {a51, a52, a53}, {a61, a62, a63}};
Flatten /@ Transpose@ArrayReshape[mat, {3, 2, 3}] // MatrixForm
$$\left( \begin{array}{ccccccccc} \text{a11} & \text{a12} & \text{a13} & \text{a31} & \text{a32} & \text{a33} & \text{a51} & \text{a52} & \text{a53} \\ \text{a21} & \text{a22} & \text{a23} & \text{a41} & \text{a42} & \text{a43} & \text{a61} & \text{a62} & \text{a63} \\ \end{array} \right)$$