This book covers an interdisciplinary field between microwave spectroscopy of electron spin resonance (ESR) and chronology science or radiation dosimetry. The main object is to determine the elapsed time with ESR from forensic medicine to the age and radiation dose in earth and space science. This book is written primarily for earth scientists as well as for archaeologists and for physicists and chemists interested in new application of the method. This book can serve as an undergraduate and graduate school textbook on applications of ESR or electron paramagnetic resonance (EPR) to geological and archaelogical dating, radiation dosimetry and microscopic magnetic resonance imaging (MRI). Introduction to ESR (EPR) and chronology science and principle of ESR dating and dosimetry are described with applications to actual problems according to materials.