We consider the multidimensional stochastic heat equation driven by a Gaussian noise which is white in time and it has an homogeneous spacial covariance. First we will define multiple stochastic integrals with respect to the noise and show their main properties. Then, we will find the explicit Wiener chaos expansion of the solution to the linear stochastic heat equation and show the convergence of the expansion in mean square, under suitable assumptions on the spacial covariance or its spectral measure. We will also establish Feynman-Kac formulas for the solution and its moments, that will be later used to derive moment estimates and intermittency properties.