Federated RDF querying systems provide an interface to multiple autonomous RDF data sources, allowing a user to execute a SPARQL query on multiple data sources at once and get one unified result. When these autonomous data sources use different vocabularies, the SPARQL query must be rewritten to the vocabulary of the data source in order to get the desired results. This thesis describes how vocabulary mappings can be used to rewrite SPARQL queries for federated RDF query processing. In this thesis, different types of vocabulary mappings are explored to find a suitable vocabulary mapping representation to use in formulating an approach for query rewriting. The approach describes how the SPARQL subqueries and solution mappings can be rewritten in order to handle heterogeneous vocabularies. The thesis then presents how the query federation engine HeFQUIN is extended to rewrite the federated queries and their results. A final evaluation of the implementation shows how implementing a query rewriting approach can improve the federated query engine’s execution times.