Lectures on algebraic quantum groups

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In September 2000, a 30-hour Advanced Course on Algebraic Quantum Groups was held at the Centre de Recerca Matematica in Barcelona. Following the course, we refined the lecture material and integrated it with background content prepared for participants, resulting in this volume. Our goal is to explore selected algebraic aspects of quantum groups. The term 'algebraic' encompasses our focus on algebraic objects, specifically quantized analogues of classical algebraic structures, rather than quantized continuous function algebras on compact groups. We emphasize the algebraic properties of these objects and their representations, using tools primarily from noncommutative algebra, representation theory, and algebraic geometry. The term 'quantum groups' refers to a vast and evolving field of mathematics and mathematical physics, which emerged from developments in theoretical physics and statistical mechanics around 1980. This field is more driven by examples than by axioms, making it challenging to define concisely. For further context, readers can refer to Chapter 1.1 and the associated references.