Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This book provides a comprehensive and accessible introduction to the latest Bayesian methods. It emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach, and is an essential primer for non-statisticians. It begins with a definition of probability and develops a step-by-step sequence of connected ideas, including basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and inference from single and multiple models. The book places less emphasis on computer coding, favoring instead a concise presentation of the mathematical statistics needed to understand how and why Bayesian analysis works. It also explains how to write out properly formulated hierarchical Bayesian models and use them in computing, research papers, and proposals. This book enables ecologists to understand the statistical principles behind Bayesian modeling and apply them to research, teaching, policy, and management.