This  paper  studies  several  aspects  of  an  important  binary  relation:   congruencemodulon.  We first introduce congruence by clarifying the division operation, and thenshow some basic properties of congruence relation and their applications in studyingproperties of integers.  After that, we shift the topic to abstract algebra, and presentsome important interpretations of congruence classes in ring theory.  Finally, we studylinear equations of congruence, carry out a proof for Chinese Remainder Theorem, andconclude the paper by stating NP-hard problems that require future attention.