What should I write in the preface of my master's thesis
You write:


What are the problems you are studying.
Why are they important.
What are your own contributions. (Maybe: "We present detailed proofs of the results...". Or maybe: "We summarize the results about A...".)
Is there anything new in your contributions? Mention that, too. Maybe you are writing in a different language, combining results that have not been explicitly combined before, providing a more detailed proof of some statement than you could find, etc.
What has been done before? A brief literature review is appropriate.


You should combine those parts in a way that feels natural. They are not section headings.

Plagiarism

To avoid plagiarism, do not copy text from elsewhere. Write in your words. This is especially true of free text, such as the introduction and literature review.

Furthermore, cite your sources. For example: "This proof follows the proof by [4], but we include additional details."

It might not be useful to rewrite theorems and definitions in your own words. If they are common knowledge (can be found in several textbooks), you can use the common ones. If the definition is less established, or if there are several variants and you have chosen to use a particular one, then a citation is appropriate, and explicitly mentioning any verbatim copying.