Explore the foundations of vertex algebras and associated varieties in this first lecture of a mini-course delivered by Anne Moreau from Université Paris-Saclay, France. Delve into the representation theory of infinite-dimensional Lie (super)algebras, quantum groups, and vertex algebras as part of the "Algebraic and Combinatorial Methods in Representation Theory" program. Gain insights into this active area of research with deep connections to mathematics and physics. Designed for graduate students, postdoctoral scholars, and researchers entering the field, this lecture forms part of a comprehensive workshop featuring four mini-courses on modern representation theory themes. Participate in this engaging session held at the International Centre for Theoretical Sciences, contributing to a major gathering of researchers in infinite dimensional Lie algebras, quantum groups, vertex algebras, and related fields.