Action principles are fundamental to physics, from classical mechanics through quantum mechanics, particle physics, and general relativity. Action principles start with an energy function called a Lagrangian describing the physical system. The accumulated value of this energy function between two states of the system is called the action. Action principles apply the calculus of variation to the action. The action depends on the energy function, and the energy function depends on the position, motion, and interactions in the system: variation of the action allows the derivation of the equations of motion without vectors or forces.

Several distinct action principles differ in the constraints on their initial and final conditions. The names of action principles have evolved over time and differ in details of the endpoints of the paths and the nature of the variation. Quantum action principles generalize and justify the older classical principles by showing they are a direct result of quantum interference patterns. Action principles are the basis for Feynman's version of quantum mechanics, general relativity and quantum field theory.

The action principles have applications as broad as physics, including many problems in classical mechanics but especially in modern problems of quantum mechanics and general relativity. These applications built up over two centuries as the power of the method and its further mathematical development rose.

This article introduces the action principle concepts and summarizes other articles with more details on concepts and specific principles.

Action principles are "integral" approaches rather than the "differential" approach of Newtonian mechanics. The core ideas are based on energy, paths, an energy function called the Lagrangian along paths, and selection of a path according to the "action", a continuous sum or integral of the Lagrangian along the path.

Introductory study of mechanics, the science of interacting objects, typically begins with Newton's laws based on the concept of force, defined by the acceleration it causes when applied to mass: ${\displaystyle F=ma.}$ This approach to mechanics focuses on a single point in space and time, attempting to answer the question: "What happens next?". Mechanics based on action principles begin with the concept of action, an energy tradeoff between kinetic energy and potential energy, defined by the physics of the problem. These approaches answer questions relating starting and ending points: Which trajectory will place a basketball in the hoop? If we launch a rocket to the Moon today, how can it land there in 5 days? The Newtonian and action-principle forms are equivalent, and either one can solve the same problems, but selecting the appropriate form will make solutions much easier.

The energy function in the action principles is not the total energy (conserved in an isolated system), but the Lagrangian, the difference between kinetic and potential energy. The kinetic energy combines the energy of motion for all the objects in the system; the potential energy depends upon the instantaneous position of the objects and drives the motion of the objects. The motion of the objects places them in new positions with new potential energy values, giving a new value for the Lagrangian.

Using energy rather than force gives immediate advantages as a basis for mechanics. Force mechanics involves 3-dimensional vector calculus, with 3 space and 3 momentum coordinates for each object in the scenario; energy is a scalar magnitude combining information from all objects, giving an immediate simplification in many cases. The components of force vary with coordinate systems; the energy value is the same in all coordinate systems. Force requires an inertial frame of reference; once velocities approach the speed of light, special relativity profoundly affects mechanics based on forces. In action principles, relativity merely requires a different Lagrangian: the principle itself is independent of coordinate systems.