Before the advent of quantum cryptography, public key cryptography techniques such as RSA, Diffie-Hellman (DH), and Elliptic Curve Cryptography (ECC) showed their importance. Whereas the discrete logarithm problem underpins the security of DH and ECC, the factorization problem serves as the foundation for RSA security. Solving these issues with the computing resources available today is thought to be challenging. Nonetheless, the quantum computer would have little trouble solving these issues. These prompts pursue alternative cryptographic algorithms that remain viable in quantum computing. The algorithms need to be efficient and secure enough in computing that not even a quantum computer should be able to solve. Many candidates are lattice-based algorithms. Most lattice-based algorithms are securely implemented with the help of Learning with Error (LWE). Much research has been done to explain how lattice-based cryptography operates using LWE. This paper provides a basic yet detailed explanation of LWE variations. The potential attacks and defenses are also discussed.