This paper presents a quantitative continuum theory of "flocking," describing the collective motion of self-propelled organisms. The model predicts the existence of an "ordered phase" where all members of a flock move in the same direction, a result of spontaneous symmetry breaking. The model accounts for long-distance, long-time behavior, including "Goldstone modes" associated with rotational symmetry breaking. These modes mix with conservation of bird number to produce propagating sound modes, leading to large density fluctuations. The model resembles the Navier-Stokes equations for fluids and a Ginsburg-Landau theory for ferromagnets. In spatial dimensions d > 4, the long-distance behavior is described by a linearized theory, while for d < 4, nonlinear effects significantly alter the behavior. In d = 2, the model predicts a true, long-range ordered state, contrasting with equilibrium systems where continuous symmetry breaking is impossible. The model also considers anisotropic cases, where birds move preferentially in a horizontal plane, leading to different predictions. The paper discusses scaling exponents, correlation functions, and the effects of anisotropy on flock dynamics. It also explores the implications of non-equilibrium effects, such as convection, which suppress velocity fluctuations and lead to anisotropic scaling. The results are validated through simulations and experiments, and the paper concludes with open questions and future research directions.This paper presents a quantitative continuum theory of "flocking," describing the collective motion of self-propelled organisms. The model predicts the existence of an "ordered phase" where all members of a flock move in the same direction, a result of spontaneous symmetry breaking. The model accounts for long-distance, long-time behavior, including "Goldstone modes" associated with rotational symmetry breaking. These modes mix with conservation of bird number to produce propagating sound modes, leading to large density fluctuations. The model resembles the Navier-Stokes equations for fluids and a Ginsburg-Landau theory for ferromagnets. In spatial dimensions d > 4, the long-distance behavior is described by a linearized theory, while for d < 4, nonlinear effects significantly alter the behavior. In d = 2, the model predicts a true, long-range ordered state, contrasting with equilibrium systems where continuous symmetry breaking is impossible. The model also considers anisotropic cases, where birds move preferentially in a horizontal plane, leading to different predictions. The paper discusses scaling exponents, correlation functions, and the effects of anisotropy on flock dynamics. It also explores the implications of non-equilibrium effects, such as convection, which suppress velocity fluctuations and lead to anisotropic scaling. The results are validated through simulations and experiments, and the paper concludes with open questions and future research directions.