Public key encryption (PKE) cryptography plays a big role in securing communication channels of internet. The security of every PKE scheme is usually based on a hard problem that has no polynomial time solution using any computational structure. However, widely used classic PKE schemes such as RSA or elliptic curve cryptography (ECC), are based on hard problems that have polynomial solutions using a quantum computer. Therefore, such PKE schemes will not be secure in post-quantum era. There exist different post-quantum PKE schemes, which rely on hard problems that do not have polynomial time solutions even using a quantum computer. Among post-quantum schemes, lattice-based cryptography and especially learning with errors (LWE) problem have gained high attention due to their low computational complexity. In addition, special cryptographic problems such as fully homomorphism have solutions based on LWE problem. In this talk, we are going to provide a general overview of lattice-based cryptography schemes and evaluate them compared to other PKE schemes.