The range of topics covered in this book has been extended significantly when compared to rather limit material usually presented on the Reynolds transport theorem (RTT) in textbooks or monographs. The material is packed into three major parts: (a) devoted to homogeneous systems, includes derivation of the RTT of the material and control volume (CV) formulations concluded by the RTT equations expressed in terms of the moving CV; (b) assigned to two-phase systems, incorporates fundamental cases namely, with storage in phases only, and with combined storage both in phases and interface split into three specific topics, among them the surface system dwelling in the interface; (c) dedicated to three-phase systems, comprises derivation a general form of the RTT that counts for both storage in phases and interface. On this basis the RTT equations for particular applications are also identified. The book is designated to support students with supplementing knowledge on fundamental concepts and methods of fluid mechanics helpful for their advanced studies. Apart from educational purposes it can be also found useful for readers working in fields of engineering or applied sciences.