Explore the foundations of cluster algebras in this comprehensive lecture on representations of acyclic quivers, Auslander-Reiten sequences, and the Caldero-Chapoton formula. Delve into key concepts including cluster algebra fundamentals, quiver representations, and essential theorems like Gabziel's theorem. Examine practical examples, work through exercises, and gain insights into main tools used in the field. Progress through definitions, propositions, and corollaries to build a solid understanding of this important area in algebraic combinatorics and representation theory.