  This chapter provides a tutorial overview of first principles methods to
describe the properties of matter at the ground state or equilibrium. It begins
with a brief introduction to quantum and statistical mechanics for predicting
the electronic structure and diverse static properties of of many-particle
systems useful for practical applications. Pedagogical examples are given to
illustrate the basic concepts and simple applications of quantum Monte Carlo
and density functional theory -- two representative methods commonly used in
the literature of first principles modeling. In addition, this chapter
highlights the practical needs for the integration of physics-based modeling
and data-science approaches to reduce the computational cost and expand the
scope of applicability. A special emphasis is placed on recent developments of
statistical surrogate models to emulate first principles calculation from a
probabilistic point of view. The probabilistic approach provides an internal
assessment of the approximation accuracy of emulation that quantifies the
uncertainty in predictions. Various recent advances toward this direction
establish a new marriage between Gaussian processes and first principles
calculation, with physical properties, such as translational, rotational, and
permutation symmetry, naturally encoded in new kernel functions. Finally, it
concludes with some prospects on future advances in the field toward faster yet
more accurate computation leveraging a synergetic combination {of} novel
theoretical concepts and efficient numerical algorithms.
