In the last 45 years, X-ray astronomy has become an integral part of modern astrophysics and cosmology. There is a wide range of astrophysical objects and phenomena, where X-rays provide crucial diagnostics. In particular they are well suited to study hot plasmas and matter under extreme physical conditions in compact objects. This book summarizes the present status of X-ray astronomy in terms of observational results and their astrophysical interpretation. It is written for students, astrophysicists as well a growing community of physicists interested in the field. An introduction including historical material is followed by chapters on X-ray astronomical instrumentation. The next two parts summarize in 17 chapters the present knowledge on various classes of X-ray sources in the galactic and extragalactic realm. While the X-ray astronomical highlights discussed in this book are mainly based on results from ROSAT, ASCA, RXTE, BeppoSAX, Chandra and XMM-Newton, a final chapter provides an outlook on observational capabilities and projects discussed for the future.