The embedding method is a powerful theoretical and computational technique that is relevant to a great many technologically and scientifically important problems. This general nature encompasses many important and topical problems in for example surface and interface electronic structure, adsorption, physics of nanostructures, molecular electronics, plasmonics and photonics, and it has become an important tool for researchers in these fields. More recently it has also been extended into the time domain. Supplemented with demonstration programmes, code and examples, this book provides a thorough review of the method and would be an accessible starting point for graduate students or researchers wishing to understand and use the method, or as a single reference source for those already familiar with the subject and applying it in their research.