Quantum computing threatens the security of classical cryptographic systems, necessitating the development of post-quantum cryptography (PQC) to secure digital communications and data. This paper explores the principles and techniques of PQC, focusing on key algorithms such as lattice-based, code-based, hash-based, and multivariate polynomial-based cryptography. The study examines the vulnerabilities of current cryptographic systems to quantum attacks, particularly through Shor's algorithm, and highlights the advancements in the NIST PQC standardization efforts. Practical implementations and performance evaluations of PQC are discussed, showcasing their resilience against quantum threats. The paper also addresses challenges in transitioning to PQC, including computational complexity and key management. Future research directions and potential advancements in PQC are outlined, emphasizing the need for continued innovation to ensure robust security in the quantum computing era.