The theory of linearized cosmological perturbations is developed in detail. First the formalism is developed for describing Gaussian isotropic stochastic processes on the sphere and homogeneous and isotropic Gaussian processes on a three-dimensional homogeneous and isotropic spatial manifold. The evolution of cosmological perturbations is derived, using both Newtonian gravity and the general theory of relativity. Issues of gauge fixing andreparameterization invariance are discussed and the use of synchronous and Newtonian gauge is presented. The scalar-vector-tensor decomposition, which block diagonalizes the equations at linear order, is discussed. Evolution assuming a single perfect fluid and multicomponent fluids is discussed. Quantities conserved on superhorizon scales are derived. The hydrodynamic approximation and its limitations are reviewed. Predictions for the matter power spectrum are discussed. Chapter appendices explain the Jeans Instability and nonlinearity, spherical wave expansions in a flat spatial geometry, and scalar harmonics for nonflat spatial geometries.