General intelligence requires quick adaption across tasks. While existing reinforcement learning (RL) methods have made progress in generalization, they typically assume only distribution changes between source and target domains. In this paper, we explore a wider range of scenarios where both the distribution and environment spaces may change. For example, in Atari games, we train agents to generalize to tasks with different levels of mode and difficulty, where there could be new state or action variables that never occurred in previous environments. To address this challenging setting, we introduce a causality-guided self-adaptive representation-based approach, called CSR, that equips the agent to generalize effectively and efficiently across a sequence of tasks with evolving dynamics. Specifically, we employ causal representation learning to characterize the latent causal variables and world models within the RL system. Such compact causal representations uncover the structural relationships among variables, enabling the agent to autonomously determine whether changes in the environment stem from distribution shifts or variations in space, and to precisely locate these changes. We then devise a three-step strategy to fine-tune the model under different scenarios accordingly. Empirical experiments show that CSR efficiently adapts to the target domains with only a few samples and outperforms state-of-the-art baselines on a wide range of scenarios, including our simulated environments, Cartpole, and Atari games.