According to Socrates in Republic’s Book IV and IX, what is justice?

(double spaced, 12pt font in Times Roman). Be as complete and concise as possible. Avoid redundancy. Do not preface your answers with superfluous introductory remarks. Answer the questions as asked. Start a new developed paragraph for each subquestion. Finally, please include 3 short quotes from Book II of the Republic wherever you deem necessary and fitting. Use only the book for information and for citing purposes. No outside resources.