The natural generalization of the quantum-mechanical N-particle wave function to relativistic space-time is a function of N space-time points, and thus of N time variables. This book, based on a collection of lectures given at a spring school in Tubingen in 2019, provides an accessible and concise introduction to the recent development of the theory of multi-time wave functions, their use in quantum field theory, their relation to detection probabilities, and the mathematical question of consistency of their time evolution equations. The book is intended for advanced students and researchers with an interest in relativity and quantum physics.