This lecture introduces Homomorphic Encryption (HE), a powerful cryptographic technique that enables computations to be performed directly on encrypted data without requiring access to a secret key, such that the decrypted result is identical to what would be obtained from computing on the original plaintext. The session covers the core concepts and mathematical foundations of HE, including additive and multiplicative homomorphism, the role of noise in fully homomorphic schemes, and practical tools such as Microsoft SEAL and HELib. Applications spanning healthcare, finance, machine learning, and cloud computing are examined alongside the key deployment challenge of computational overhead.