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This book studies the evolution of scalar cosmological perturbations in the 1+3 Covariant Gauge-Invariant formalism for generic f(R) theories of gravity. It provides with a complete set of equations describing the evolution of matter and curvature fluctuations for a multi-fluid cosmological medium. It also deals with a specific model of a radiation-dust fluid universe described by barotropic equations of state where the perturbation equations are applied around a background solution of a specific toy model of gravity and looks at exact solutions for scales much smaller and much larger than the Hubble radius.