We introduce a self-supervised speech pre-training method called TERA, which stands for Transformer Encoder Representations from Alteration. Recent approaches often learn through the formulation of a single auxiliary task like contrastive prediction, autoregressive prediction, or masked reconstruction. Unlike previous approaches, we use a multi-target auxiliary task to pre-train Transformer Encoders on a large amount of unlabeled speech. The model learns through the reconstruction of acoustic frames from its altered counterpart, where we use a stochastic policy to alter along three dimensions: temporal, channel, and magnitude. TERA can be used to extract speech representations or fine-tune with downstream models. We evaluate TERA on several downstream tasks, including phoneme classification, speaker recognition, and speech recognition. TERA achieved strong performance on these tasks by improving upon surface features and outperforming previous methods. In our experiments, we show that through alteration along different dimensions, the model learns to encode distinct aspects of speech. We explore different knowledge transfer methods to incorporate the pre-trained model with downstream models. Furthermore, we show that the proposed method can be easily transferred to another dataset not used in pre-training.