This book is intended for practicing experts in the financial arena, in particular actuaries in the field of property-casualty insurance, life insurance, reinsurance and insurance supervision, as well as teachers and students. The book provides a thorough exploration of Credibility Theory covering most aspects of this topic from the simplest case to the most detailed dynamic model. Because credibility is a lifeless topic if it is not linked closely to practical applications, the book treats explicitly the tasks which the actuary encounters in daily work: estimation of loss ratios, claim frequencies and claim sizes.