This chapter covers the implementation of field theory in curved manifolds. It begins with General Relativity and its classical tests in the solar system, followed by a brief discussion on gravitational waves. Cosmology is introduced as the study of the Universe’s large-scale structure based on three assumptions: gravitation theory, the nature of matter, and symmetry. The chapter traces modern cosmology’s development from Einstein’s general relativity and the cosmological constant to the Big Bang theory, supported by Hubble’s expanding Universe and cosmic microwave background radiation. Redshift measurements help determine the Universe’s expansion rate and age. The cosmological constant is now crucial for explaining the accelerating expansion. Scalar and spinor fields are adapted to curved spacetime using tetrads, and the coupling between electrodynamics and gravitation is explored. The chapter concludes with the Einstein-Cartan formulation of gravitation and includes exercises for practical applications.