This course represents the fundamentals on the working principles of all main components of the modern microscopes such as electron and ion optics as well as diverse signal detectors, on the physics of the particle interaction with the matter and of the image formation in different operation modes. The obtained knowledge will serve as basics for future practical usage of electron and ion microscopy as well as focused ion beam systems in various fields from basic research to industrial applications. A distinguished feature of the course is the consideration of both electron and ion beam technologies, which started to be rapidly growing due to the availability of recently industrially developed dual beam equipment, where these technologies are used jointly.