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

$$\left( \begin{array}{ccccccccc} \text{a11} & \text{a12} & \text{a13} & \text{a31} & \text{a32} & \text{a33} & \text{a51} & \text{a52} & \text{a53} \\ \text{a21} & \text{a22} & \text{a23} & \text{a41} & \text{a42} & \text{a43} & \text{a61} & \text{a62} & \text{a63} \\ \end{array} \right)$$