This book discusses the methods used in helio- and asteroseismology for the collection, analysis and interpretation of data. It is the first comprehensive discussion of helioseismic and asteroseismic methodology, collecting techniques from over 300 research papers spread out over decades, with a critical discussion and inter-comparison. It enables the reader to follow the path of inference from the collection of the data at the telescope through to the understanding gained in terms of the modeling of solar and stellar physics and stellar evolution. By focusing on how results are obtained, rather than on the results themselves, this book provides the essential background needed to understand this field, which is rapidly advancing due to the availability of modern observing facilities both on the ground and in space. The material is accessible for advanced undergraduates and post-graduates, and provides an essential resource for researchers in the field.