Explore advanced concepts in commutative group theory in this 32-minute lecture from the Insights into Mathematics series. Delve into the fundamental structure theorem, which states that every commutative group is isomorphic to a direct sum of cyclic groups Z_n. Examine key notions such as isomorphisms, homomorphisms, cosets of subgroups, and the process of forming quotient groups. Gain a deeper understanding of these essential algebraic structures and their relationships, enhancing your knowledge of abstract algebra and laying the groundwork for further study in algebraic topology.