  We introduce Hadamard matrices whose entries are quaternionic. We then go on
to provide classification of quaternionic Hadamard matrices of circulant core
of orders 2 through 5. We also introduce quaternionic Hadamard matrices of
Butson type and ways to create quaternionic Hadamard matrices from real and
complex Hadamard matrices. Examples are shown that showcase how Hadamard
matrices over the quaternions are richer than Hadamard matrices over the
complex numbers.
