This is an introductory course on plasma-based acceleration, including laser wakefield and plasma wakefield acceleration. The course will introduce students to the physics of how lasers and charged particle beams propagate through plasmas, how they excite plasma wave wakefields, and how particles are loaded into and are accelerated in these wakefields. The nomenclature of the subject will be introduced and why this topic is currently of great interest will be explained. This course is suitable for graduate students or upper division undergraduate students with an interest in this promising multi-disciplinary field. The course is also appropriate for physicists or engineers working in accelerator-related fields who wish to familiarize themselves with plasma-based accelerator concepts.