Challenges of Astronomy in a unique collection of thirty astronomy experiments ranging from ancient astronomy to cosmology. Each of the experiments contains one or more challenges for the reader. The progression is from the Earth outward through the solar system to the stellar and galactic realm. Topics include the shape of the sky, Stonehenge as a stoneage abacus, determination of the size of the Earth, the distance of the Moon and planets, Kepler's laws, planetary mass and density, the temperatures and atmospheres of planets, the speed of light, the distances of stars, the nature of the quiet and active Sun, photometry and spectroscopy, stars clusters and variable stars, fundamental properties of stars, and Olber's paradox. Challenges of Astronomy is a translation and extensive revision of a German-language resource book for secondary school teachers of science. Physical science teachers will find this edition too a rich resource of experiments to their own milieus, but it is suitable for many other English-language readers too, from northern and southern hemisphere locations. The beginning experiments are suitable for bright high school and non-science major university students while the later experiments which offer increasingly difficult challenges are more suitable for sciences majors. Amateurs with a variety of skills will find this hands-on book entertaining, informative, and useful.