In recent years, an increasing number of organizations and individuals have contributed to the Semantic Web by publishing data according to the Linked Data principles. In addition, a significant body of Semantic Web research exists that studies various aspects of knowledge representation and automated reasoning over collections of such data. However, a challenge that is crucial for achieving the vision of a Semantic Web - but that has not yet been studied to a comparable extent - is to enable automated software agents to operate directly on decentralized Linked Data that is distributed over the WWW. In particular, fundamental questions related to querying this data on the WWW have received very limited research attention. This book contributes towards filling this gap by studying the foundations of declarative queries over Linked Data on the WWW. Our particular focus in this book are approaches to use the SPARQL query language and execute queries by traversing Linked Data live during the query execution process. More specifically, we first provide formal foundations to adapt SPARQL to the given context. Thereafter, we use an abstract machine model to formally show computational feasibility and related properties of the resulting types of SPARQL queries. Additionally, we investigate fundamental properties of applying the traversal-based approach to query execution that is tailored to the use case of querying Linked Data directly on the WWW. The author, Olaf Hartig, has won the Semantic Web Science Association (SWSA) Distinguished Dissertation Award for this publication.