The task of a recommender system is to take a list of all possible items and rank them according to preferences of particular users. This ranked list is referred to as a personalized ranking, or, more often, as a recommendation.
For example, a shopping website may have a section with recommendations where users can see items that they may find relevant and could decide to buy. Websites selling tickets to concerts may recommend interesting shows, and an online music player may suggest songs that the user is likely to enjoy. Or a website with online courses, such as Coursera.org, may recommend a course similar to ones the user has already finished:
The recommendations are typically based on historical data: the past transaction history, visits, and clicks that the users have made. So, a recommender system is a system that takes...