The paper introduces TeVeS, a relativistic gravitational theory inspired by Milgrom's modified Newtonian dynamics (MOND) paradigm. TeVeS aims to resolve the issues with previous relativistic MOND theories, such as the violation of causality and the underestimation of gravitational lensing. The theory is based on a metric, a scalar field, and a 4-vector field, all of which are dynamical. It has a Newtonian limit for nonrelativistic dynamics with significant acceleration and a MOND limit for small accelerations. The theory passes solar system tests, predicts gravitational lensing without requiring dark matter, and does not exhibit superluminal propagation. Cosmological models based on TeVeS are similar to those based on general relativity, with the scalar field evolving slowly. The paper also discusses the implications of TeVeS for cosmology and the possibility of ruling out superluminal propagation.The paper introduces TeVeS, a relativistic gravitational theory inspired by Milgrom's modified Newtonian dynamics (MOND) paradigm. TeVeS aims to resolve the issues with previous relativistic MOND theories, such as the violation of causality and the underestimation of gravitational lensing. The theory is based on a metric, a scalar field, and a 4-vector field, all of which are dynamical. It has a Newtonian limit for nonrelativistic dynamics with significant acceleration and a MOND limit for small accelerations. The theory passes solar system tests, predicts gravitational lensing without requiring dark matter, and does not exhibit superluminal propagation. Cosmological models based on TeVeS are similar to those based on general relativity, with the scalar field evolving slowly. The paper also discusses the implications of TeVeS for cosmology and the possibility of ruling out superluminal propagation.