In this paper, we formally define the problem of representing and leveraging abstract event causality to power downstream applications. We propose a novel solution to this problem, which build an abstract causality network and embed the causality network into a continuous vector space. The abstract causality network is generalized from a specific one, with abstract event nodes represented by frequently cooccurring word pairs. To perform the embedding task, we design a dual cause-effect transition model. Therefore, the proposed method can obtain general, frequent, and simple causality patterns, meanwhile, simplify event matching. Given the causality network and the learned embeddings, our model can be applied to a wide range of applications such as event prediction, event clustering and stock market movement prediction. Experimental results demonstrate that 1) the abstract causality network is effective for discovering high-level causality rules behind specific causal events; 2) the embedding models perform better than state-of-the-art link prediction techniques in predicting events; and 3) the event causality embedding is an easy-to-use and sophisticated feature for downstream applications such as stock market movement prediction.