* First book on the subject at the undergraduate level * Quick introduction to many major topics in fundamental theoretical physics suitable for undergraduate courses * High interest currently in quantum gravity among physicists worldwide * Controversial subject which needs good, impartial introduction from respected scientists This book provides an accessible introduction to loop quantum gravity and some of its applications, at a level suitable for undergraduate students and others with only a minimal knowledge of college level physics. In particular it is not assumed that the reader is familiar with general relativity and only minimally familiar with quantum mechanics and Hamiltonian mechanics. Most chapters end with problems that elaborate on the text, and aid learning. Applications such as loop quantum cosmology, black hole entropy and spin foams are briefly covered. The text is ideally suited for an undergraduate course in the senior year of a physics major. It can also be used to introduce undergraduates to general relativity and quantum field theory as part of a 'special topics' type of course. Table Of Contents 1: Why quantize gravity 2: Special relativity and electromagnetism 3: Some elements of general relativity 4: Hamiltonian mechanics including constraints and fields 5: Yang-Mills theories 6: Quantum mechanics and elements of quantum field theories 7: General relativity in terms of Ashtekar's variables 8: Loop representation for general relativity 9: An application: loop quantum cosmology 10: Further developments 11: Open issues and controversies