This book provides a complete overview of the development of cosmic ray physics, with historical and educational considerations, from early evidence of the existence of extraterrestrial radiation up to the most recent applications of cosmic ray muons in different aspects of daily life. Many of the original results that contributed to the study of cosmic radiation are presented and discussed, accompanied by bibliographic references, numerous in-depth appendices, about 200 illustrations and a large chapter dedicated to the overall impact of cosmic rays. The book includes sections on, among other topics: the debate on the corpuscular or radiative nature of cosmic radiation; the development of early techniques for detecting cosmic particles; the properties and composition of primary and secondary radiation; and the interaction of cosmic muons in matter and a long list of their recent applications, ranging from the muon tomography techniques to the investigation of the stability of civil buildings. The book is addressed to a wide audience, and thus, while it is used for introductory cosmic ray physics courses at the bachelors or masters level, high school students and teachers involved in educational projects around cosmic rays also benefit from its many historical and educational aspects.