In this thesis, we give the maximal rank (the best possible upper bound) of quaternionic tensors in the some small cases. Decomposition of a quaternionic tensor into simple tensors in the some of these cases are discussed. We also give an example of a complex tensor that has different ranks over the complex field and the real quaternion algebra.

Moreover, we give the maximal rank and canonical forms of arbitrary quaternionic 3-tensors with 2 frontal slices. We also discuss some upper bounds for general quaternion tensors by using a block tensor approach.