This thesis explores the representations of finite groups on finite-dimensional vector spaces. It is structured into three stand-alone chapters. The first chapter provides an overview of the algebraic structures that stand behind the theory of representations. The second chapter offers an extensive review of the theory of representations from various perspectives and proves several key properties. The final chapter is dedicated to the application of the theory, where representations are examined through the specific example of the space of parking functions. The thesis covers a broad range of topics, ultimately enabling the reader to understand how to describe the structure of all irreducible representations of the symmetric group, both in terms of character theory and through the lens of symmetric functions.
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