An introduction to string states and their interactions

The subject matter of these lecture notes is the open bosonic critical string, its perturbative spectrum and interactions. We begin with a brief review of classical string propagation, quantization, as well as the level-by-level construction of physical string states. We then review a new, covariant and efficient technology of constructing entire trajectories of infinitely many physical states deeper in the string spectrum. Finally, elements of the calculation of string scattering amplitudes, including aspects of the application of the technology for the efficient calculation of tree-level amplitudes of deeper trajectories, are also covered. The material is based on three invited lectures delivered by the author at the 2024 Modave Summer School in Mathematical Physics.