The mating game plays a central role in promoting individual biological fitness, but many other life-history traits (physical, physiological, and behavioral)  also influence fitness.  This book is about the optimal method for measuring biological fitness in mammals. This involves measuring lifetime reproductive success of individuals that survive to breeding age while living freely in nature.  Constant monitoring of individuals is required, which explains why such studies are difficult to conduct and rare.  I use a long-term study of extremely polygynous northern elephant seals (over 62 continuous years) to illustrate the necessary operations, benefits, pitfalls, and difficulties in conducting such studies.  The aim of this treatise is to inform and facilitate future investigations of other animals. The Quest for Darwinian Fitness: Case Studies of Elephant Seals is a long-term study of the lifetime reproductive success of individuals, a practical approach to determining biological fitness.  This case study is based on an animal that has been studied intensively.  The aim of this chronicle is to facilitate the future long-term of other animals.