They say a piece of paper can’t decide your future, but it can surely describe your past. Whether you are cold emailing or working on your application package, you surely require a Curriculum Vitae (CV) to attach. Unlike job applications, where you submit your 1-2 page Resume, a CV lets you brag about your experience and achievements with no page limit. But ideally try limiting it to 3 pages. Some universities might specify 2 pages so you can trim your master 3 pager accordingly.
Even though there are multiple formats floating around on the internet, my personal favorite is a plain, classic US format as attached below. Some use formats that have fancy colors or have their photos embedded. Honestly, let the reader set up a meeting to see your face rather than making your CV an Instagram profile. Though you can provide links to your relevant communication channels such as LinkedIn, Gmail, GitHub, Google Scholar, etc. beneath your name at the top. The rest of the information can be clustered into different categories with headings such as Educational Background, Research or Industry Experience, Key Projects, etc. I will discuss a couple of these subcategories in depth in the subsequent paragraphs.
With this, we have addressed the first elephant in the room. For the next one, jump to the next chapter.