Mathematics: Research

When you paraphrase something, you rewrite someone else's idea using your own words, giving the original author credit for the idea. Paraphrasing is shorter than summarizing because you focus only a single idea and not the entire work.

When you plagiarize something, you take someone else's words or ideas and use them as your own without giving credit to the original author. You do not have to give credit for common knowledge (eg., historical facts).

When you quote something, you use the exact same words as the original author, putting them in "quotation marks" and matching each word exactly as it appears in the work. Quotes should be kept short and used only rarely, and you must always give credit to the original author.

When you summarize something, you give a brief description of the work or the author's main idea(s), using your own words. Credit must always be given to the original author.