well, I've recently found myself interested in the subject, I hadn't studied the subject in high school and I haven't taken the course in university yet but since I've read Herstein's abstract algebra book I have become familiar with some congruence equations and other simple stuff. Right now I'm studying Gauss's Disquisitiones Arithmeticae and It seems so fascinating to me. Somewhere I read a comment made by Gauss that says 'Mathematics is the mother of all sciences and number theory is the mother of mathematics', so, If a giant like Gauss believes number theory is that important in mathematics, then it must be! The thing is I don't know why number theory is that important. I understand that many concepts in group theory and abstract algebra are in fact generalizations of the properties of integers that have originated from the works of 18th and 19th century mathematicians in number theory but I don't know how number theory is researched these days. It seems that modern number theory is way more complicated than the naive number theory. Would someone give a short introduction to number theory here? Why It is so important as Gauss says? I've heard that all great mathematicians were good number theorists, from Euler, Gauss, Eisenstein, Galois and other great 19th century mathematicians to contemporary mathematicians like Emil Artin, G.H. Hardy, Paul Erdos, all of them were strong mathematicians in number theory. so If someone tells me about number theory more, I'd really appreciate that.