The study of planet formation has been revolutionized by recent observational breakthroughs, which have allowed the detection and characterization of extrasolar planets, the imaging of protoplanetary disks, and the discovery of the Solar System's Kuiper Belt. Written for beginning graduate students, this textbook provides a basic understanding of the astrophysical processes that shape the formation of planetary systems. It begins by describing the structure and evolution of protoplanetary disks, moves on to the formation of planetesimals, terrestrial and gas giant planets, and concludes by surveying new theoretical ideas for the early evolution of planetary systems. Covering all phases of planet formation - from protoplanetary disks to the dynamical evolution of planetary systems - this introduction can be understood by readers with backgrounds in planetary science, and observational and theoretical astronomy. It highlights the physical principles underlying planet formation and the areas where more research and new observations are needed.