Cryptanalysis and Euler Theorem Questions Essay Assignment

I need an explanation for this Engineering question to help me study.
What are cryptography and cryptanalysis?
What is earlier reason for the use of cryptography?
Fermat’s theorem and Euler’s theorem are the two theorems that play important roles in public-key cryptography. Explain each theorem in details their roles in public-key cryptography.
Explain the Chinese Remainder Theorem that have been discovered by the Chinese mathematician Agrawal in 100 A.D.