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Group representation theory investigates connections between groups and mathematical objects, with classical representation theory focusing on linear automorphism groups of complex vector spaces and modular representation theory considering actions on vector spaces over fields with positive characteristic. Block theory is a key area within modular representation theory, involving the decomposition of finite group algebras into indecomposable direct algebra factors called block algebras. The block algebras of a finite group algebra are investigated individually, with the goal of understanding how the structure theory of finite groups and the representation theory of block algebras inform each other. Block theory seeks to classify source algebras of blocks with a fixed defect group, which has been achieved in two cases: blocks with cyclic and Klein four defect groups. The local structure of a block algebra includes invariants such as a defect group, fusion system, and class, while the global structure includes invariants such as the numbers of simple modules, module categories, and derived categories.