The linear perturbation theory of Friedman universes is treated in a gauge-invariant manner (i.e., invariant under linearized coordinate transformations). After presenting some mathematical tools in Chapter 1, the perturbation equations are derived with the help of the 3+1 formalism of general relativity in Chapter 2. Bardeens perturbation theory [4] is thereby extended to the treatment of collisionless matter. In Chapter 3 we solve the perturbation equations for perfect fuids explicitely. The results are applied to the discussion of the Sachs-Wolfe effet and of the traditional baryonic scenario of galaxy formation. In Chapter 4 numerical solutions of the gauge invariant perturbation equations are presented for a universe consisting of collisionless particles of mass mx ≠ 0, massless neutrinos and radiation. In this scenarios the masses of the first objects to collapse are of the order of m³pl/m²x. Within the gauge-invariant treatment, the perturbation amplitudes exhibit no growth on scales which are larger than the present horison size.