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The high expressiveness and elasticity of the graph data model brought the scientific community to rely on graphs to model real-world processes. As a consequence, many graph query languages have been designed to extract useful information from graphs. Many solutions have been proposed from both industries, such as Cypher and PGQL, and academia, such as G-CORE. Among them, Cypher has been shown to be useful and applicable in many scenarios and it is currently a reference point in the ISO standardization process of GQL, the new Graph Query Language standard. However, in a world where data continuously flow, users are more and more interested in continuously querying data, aiming at exploiting temporal based information. Cypher is not adequate for dealing with streams of graphs and continuous query evaluation. First, it does not acknowledge the temporal dimension of the data, and consequently, it does not offer direct support for time filters definition in queries. Moreover, it only supports to issue each query once, forcing the user to manually submit the query again to check for changes in the results. This thesis focuses on extending the syntax and the semantics Cypher to handle streams of graphs and continuous queries and provide a formal framework to check the correctness and completeness over time of continuous queries over streams of graphs.