"Fundamentals of Stochastic Filtering" is a specialized book that deals with the theory of stochastic filtering, a process that allows for meaningful inferences about evolving systems from incomplete observations and stochastic models. This book is aimed at a wide audience, from students to experienced researchers, who wish to familiarize themselves with the fundamental concepts and methods of stochastic filtering. The content is presented in a way that is suitable for both self-study and as teaching material for graduates. Most of the fundamental results are presented using modern methods that facilitate easy reference. Additionally, the book contains numerous exercises with solutions that enhance the understanding of the topics covered. The theory of stochastic filtering in continuous time is supported by measure theory, stochastic processes, and stochastic calculus, with basic knowledge of measure theory and probability assumed.