Over recent years, astronomy and cosmology have made extraordinary progress in addressing and solving many fundamental problems, opening up new areas of physical enquiry. This book provides a comprehensive study of these developments, emphasising the synergies between observation and theory, from the very early Universe to the study of exoplanets. It focuses on how a vast range of physical processes and techniques may be applied to understanding current problems of modern astrophysics and cosmology. Coverage spans the whole of the electromagnetic spectrum, as well as astroparticle physics, incorporating cosmic rays, neutrino astronomy, dark matter and dark energy studies and gravitational waves. The book is written for final-year undergraduates and first-year graduate students in the physical sciences, with an appropriate level of mathematics, to help them prepare for carrying out frontier research in astrophysics and cosmology.