Abstract: There is a reason that Spotify is still around after three of the biggest companies in the world: Apple, Google, and Amazon; have all stepped into the music streaming industry. They are able to recommend better music to me than anyone else. At first, I thought I was biased in believing this, as I am a loyal Spotify user. However, in doing research, I have come to find that Spotify does, in fact, have a much better system than the other three. They use three styles of models to recommend music. The first is Natural Language Processing models. These compare songs based on words used to describe the songs via things such as articles on the web. The next is used to recommend songs that aren’t as popular. These Content Based models look at the actual audio and use similarities to recommend similar songs to you. The last style is known as Collaboration Filtering. Essentially what it is doing is creating a User vector for every User and a song vector for every song. It then compares them to recommend music that is similar to each other and music that similar users listen to. Throughout this paper, I will discuss Collaboration Filtering as it is by far the most popular and is at the heart of Spotify’s most popular music recommendation method: Discover Weekly. My focus will be on this algorithm and more specifically how linear algebra is used to power it. Afterward, I will create a simple recommendation system of my own to examine the Collaboration Filtering even more. It must be noted that a similar approach to Spotify’s model is used by other companies such as Last.fm and another has been popularized by the Netflix Prize. I will solely be exploring Spotify’s Collaboration Filtering method which differs from Netflix in that it uses mostly implicit feedback as opposed to Netflix’s more explicit feedback approach using ratings other explicit user data.