Dive into the world of trapped ion quantum computers with this comprehensive lecture, the first in a series of four, delivered by Thomas Monz from the University of Innsbruck, Austria. Explore the fundamental principles and cutting-edge developments in this exciting field of quantum computation. Learn about the unique properties of trapped ions, their potential for quantum information processing, and the challenges faced in building scalable quantum systems. Gain insights into the current state of trapped ion quantum computing research and its implications for future technological advancements. This in-depth presentation, part of the ICTP-SAIFR School on Quantum Computation held in November 2022, offers a valuable opportunity to expand your knowledge of quantum computing and its potential applications.