This book makes accessible the basic principles and ideas of modern cosmological theory to undergraduates in mathematics, physics and related areas of study. The areas covered include observations, expansion of the universe, cosmological problems, formation of structure, production of helium in the early universe and inflationary models of the origin of the universe. There is an accessible treatment of inflationary theory, black holes, magnetic monopoles and boson stars. The dark matter debate is also discussed and detailed exercises are provided at the end of each chapter.Previous knowledge of relativity or quantum field theory is not required; rather the book provides a detailed exposition of how cosmological theory has developed. The author aims to encourage students to develop their own insights into cosmology.