We introduce a novel physical layer scheme for single user Multiple-Input Multiple-Output (MIMO) communications based on unsupervised deep learning using an autoencoder. This method extends prior work on the joint optimization of physical layer representation and encoding and decoding processes as a single end-to-end task by expanding transmitter and receivers to the multi-antenna case. We introduce a widely used domain appropriate wireless channel impairment model (Rayleigh fading channel), into the autoencoder optimization problem in order to directly learn a system which optimizes for it. We considered both spatial diversity and spatial multiplexing techniques in our implementation. Our deep learning-based approach demonstrates significant potential for learning schemes which approach and exceed the performance of the methods which are widely used in existing wireless MIMO systems. We discuss how the proposed scheme can be easily adapted for open-loop and closed-loop operation in spatial diversity and multiplexing modes and extended use with only compact binary channel state information (CSI) as feedback.