  Aiming for simplicity of explicit equations and at the same time controllable
accuracy of the theory we present results for all thermodynamic quantities and
correlation functions for the weakly interacting Bose gas at
short-to-intermediate distances obtained within an improved version of
Beliaev's diagrammatic technique. With a small symmetry breaking term Beliaev's
diagrammatic technique becomes regular in the infrared limit. Up to
higher-order terms (for which we present order-of-magnitude estimates), the
partition function and entropy of the system formally correspond to those of a
non-interacting bosonic (pseudo-)Hamiltonian with a temperature dependent
Bogoliubov-type dispersion relation. Away from the fluctuation region, this
approach provides the most accurate--in fact, the best possible within the
Bogoliubov-type pseudo-Hamiltonian framework--description of the system with
controlled accuracy. It produces accurate answers for the off-diagonal
correlation functions up to distances where the behaviour of correlators is
controlled by generic hydrodynamic relations, and thus can be accurately
extrapolated to arbitrarily large scales. In the fluctuation region, the
non-perturbative contributions are given by universal (for all weakly
interacting U(1) systems) constants and scaling functions, which can be
obtained separately--by simulating classical U(1) models--and then used to
extend the description of the weakly interacting Bose gas to the fluctuation
region. The theory works in all spatial dimensions and we explicitly check its
validity against first-principle Monte Carlo simulations for various
thermodynamic properties and the single-particle density matrix.
