An order of precedence is a sequential hierarchy of nominal importance of items. Most often it is used in the context of people by many organizations and governments, for very formal and state occasions, especially where diplomats are present. It can also be used in the context of decorations, medals and awards. Historically, the order of precedence had a more widespread use, especially in court and aristocratic life.

One's position in an order of precedence is not necessarily an indication of functional importance, but rather an indication of ceremonial or historical relevance; for instance, it may dictate where dignitaries are seated at formal dinners. The term is occasionally used to mean the order of succession to determine who replaces the head of state in the event he or she is removed from office or incapacitated.

What follow are general orders of precedence for different countries for state purposes such as diplomatic dinners, and may assume such functions are held in the capital. When they are held in another city or region, local officials such as governors would be much higher up the order. There may also be more specific and local orders of precedence, for particular occasions or within particular institutions. Universities and the professions often have their own rules of precedence applying locally, using (for example) on university or professional rank, each rank then being ordered within itself on the basis of seniority (i.e. date of attaining that rank). Within an institution the officials of that institution are likely to rank much higher in the order than in a general order of precedence - the chancellor or president of a university may well precede anyone except a head of state for example. The same might be true for a mayor in his own city.

In mathematics, big O notation is used to describe the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called Landau notation, Bachmann–Landau notation (after Edmund Landau and Paul Bachmann), or asymptotic notation. In computer science, big O notation is used to classify algorithms by how they respond (e.g., in their processing time or working space requirements) to changes in input size.

Big O notation characterizes functions according to their growth rates: different functions with the same growth rate may be represented using the same O notation. A description of a function in terms of big O notation usually only provides an upper bound on the growth rate of the function. Associated with big O notation are several related notations, using the symbols o, Ω, ω, and Θ, to describe other kinds of bounds on asymptotic growth rates.

Big O notation is also used in many other fields to provide similar estimates.