This paper proposes non-coherent multiple-input multi-ple-output (MIMO) communication systems employing per transmit antenna differential mapping (PADM), which generates an independent differentially encoded sequence for each of the multiple transmit antennas by means of space-time coding and mapping. At a receiver, the proposed PADM employs adaptive maximum-likelihood detection (MLD). The features of PADM are as follows: 1) it has excellent tracking performance for fast time-varying fading channels, because it can detect transmitted data without needing channel state information (CSI); 2) it can be applied not only to transmit diversity (TD) but also to spatial multiplexing (SM). In this paper, we analyze the adaptive MLD based on pseudo matrix inversion and derive its metric for data detection. In order to satisfy requirements on multiple transmitted sequences for the adaptive MLD, this paper proposes a mapping rule for PADM. Next, this paper describes a receiver structure based on per-survivor processing (PSP), which can drastically reduce the complexity of adaptive MLD. Finally, computer simulations confirm that the proposed non-coherent MIMO communication systems employing PADM have excellent tracking capability for TD and SM on fast time-varying fading channels.