An order-dependent query is one whose result (interpreted as a multiset) changes if the order of the input records is changed. In a stock-quotes database, for instance, retrieving all quotes concerning a given stock for a given day does not depend on order, because the collection of quotes does not depend on order. By contrast, finding a stock's fiveprice moving-average in a trades table gives a result that depends on the order of the table. Query languages based on the relational data model can handle order-dependent queries only through add-ons. SQL:1999, for instance, has a new "window" mechanism which can sort data in limited parts of a query. Add-ons make order-dependent queries difficult to write and to optimize. In this paper we show that order can be a natural property of the underlying data model and algebra. We introduce a new query language and algebra, called AQuery, that supports order from-theground-up. New order-related query transformations arise in this setting. We show by experiment that this framework - language plus optimization techniques - brings orders-ofmagnitude improvement over SQL:1999 systems on many natural order-dependent queries.