The field of beam physics touches many areas of physics, engineering, and the sciences. In general terms, beams describe ensembles of particles with initial conditions similar enough to be treated together as a group so that the motion is a weakly nonlinear perturbation of a chosen reference particle. Particle beams are used in a variety of areas, ranging from electron microscopes, particle spectrometers, medical radiation facilities, powerful light sources, and astrophysics to large synchrotrons and storage rings such as the LHC at CERN. An Introduction to Beam Physics is based on lectures given at Michigan State University's Department of Physics and Astronomy, the online VUBeam program, the U.S. Particle Accelerator School, the CERN Academic Training Programme, and various other venues. It is accessible to beginning graduate and upper-division undergraduate students in physics, mathematics, and engineering. The book begins with a historical overview of methods for generating and accelerating beams, highlighting important advances through the eyes of their developers using their original drawings. The book then presents concepts of linear beam optics, transfer matrices, the general equations of motion, and the main techniques used for single- and multi-pass systems. Some advanced nonlinear topics, including the computation of aberrations and a study of resonances, round out the presentation.