Mathematical Background, Partial Homomorphic Encryption Schemes (Paillier and Damgard-Jurik Encryption Schemes), Lattice-Based Cryptography, Ring-LWE problem, the LLL Algorithm, Homomorphic Encryption Schemes (BGV, BFV, CKKS), Bootstrapping, Scheme Switching, Multi-key Homomorphic Encryption, Applications of Homomorphic Encryption on Machine Learning, Acceleration of NTT Algorithm for Homomorphic Encryption