This book provides a thorough introduction to asymptotic inference. It begins with an elementary treatment of one-parameter statistical models and goes on to discuss basic properties of curved exponential families, the Fisher-Efron-Amari theory and Jeffreys-Rao Riemannian geometry based on Fisher information. It also provides an overview of recent developments in the field.Classifies and introduces additional work in the field.-- Several appendices provide useful mathematical material on basic concepts in differential geometry.