A survey on temporal knowledge graph: representation learning and applications Temporal knowledge graphs (TKGs) incorporate time information into knowledge graphs (KGs) to model the dynamic evolution of entities and relations over time. Unlike static KGs, TKGs include timestamps, allowing for more accurate representation of facts that change over time. This paper provides a comprehensive survey of TKG representation learning methods and their applications. It begins with an introduction to the definitions, datasets, and evaluation metrics for TKG representation learning. Next, it proposes a taxonomy based on the core technologies of TKG representation learning methods and provides an in-depth analysis of different methods in each category. Finally, it presents various downstream applications related to TKGs, including temporal knowledge graph reasoning, entity alignment, and question answering. The paper concludes with an outlook on future research directions in this area. Key contributions include an extensive investigation of various TKG representation learning methods, a new classification taxonomy, and a detailed analysis of ten distinct categories of methods. The paper also introduces the latest developments in TKG applications and summarizes existing research, pointing out future directions for further work. The paper is organized as follows: Chapter 2 introduces the background of TKGs, including definitions, datasets, and evaluation metrics. Chapter 3 summarizes various TKG representation learning methods, including transformation-based, decomposition-based, graph neural networks-based, capsule network-based, autoregression-based, temporal point process-based, interpretability-based, language model-based, and few-shot learning-based methods. Chapter 4 introduces related applications of TKGs, such as temporal knowledge graph reasoning, entity alignment, and question answering. Chapter 5 highlights future directions in TKG representation learning, including scalability, interpretability, information fusion, and the integration of large language models. Chapter 6 concludes the paper.A survey on temporal knowledge graph: representation learning and applications Temporal knowledge graphs (TKGs) incorporate time information into knowledge graphs (KGs) to model the dynamic evolution of entities and relations over time. Unlike static KGs, TKGs include timestamps, allowing for more accurate representation of facts that change over time. This paper provides a comprehensive survey of TKG representation learning methods and their applications. It begins with an introduction to the definitions, datasets, and evaluation metrics for TKG representation learning. Next, it proposes a taxonomy based on the core technologies of TKG representation learning methods and provides an in-depth analysis of different methods in each category. Finally, it presents various downstream applications related to TKGs, including temporal knowledge graph reasoning, entity alignment, and question answering. The paper concludes with an outlook on future research directions in this area. Key contributions include an extensive investigation of various TKG representation learning methods, a new classification taxonomy, and a detailed analysis of ten distinct categories of methods. The paper also introduces the latest developments in TKG applications and summarizes existing research, pointing out future directions for further work. The paper is organized as follows: Chapter 2 introduces the background of TKGs, including definitions, datasets, and evaluation metrics. Chapter 3 summarizes various TKG representation learning methods, including transformation-based, decomposition-based, graph neural networks-based, capsule network-based, autoregression-based, temporal point process-based, interpretability-based, language model-based, and few-shot learning-based methods. Chapter 4 introduces related applications of TKGs, such as temporal knowledge graph reasoning, entity alignment, and question answering. Chapter 5 highlights future directions in TKG representation learning, including scalability, interpretability, information fusion, and the integration of large language models. Chapter 6 concludes the paper.