  We extend the No-Core Shell Model (NCSM) methodology to incorporate
strangeness degrees of freedom and apply it to single-$\Lambda$ hypernuclei.
After discussing the transformation of the hyperon-nucleon (YN) interaction
into Harmonic-Oscillator (HO) basis and the Similarity Renormalization Group
transformation applied to it to improve model-space convergence, we present two
complementary formulations of the NCSM, one that uses relative Jacobi
coordinates and symmetry-adapted basis states to fully exploit the symmetries
of the hypernuclear Hamiltonian, and one working in a Slater determinant basis
of HO states where antisymmetrization and computation of matrix elements is
simple and to which an importance-truncation scheme can be applied. For the
Jacobi-coordinate formulation, we give an iterative procedure for the
construction of the antisymmetric basis for arbitrary particle number and
present the formulae used to embed two- and three-baryon interactions into the
many-body space. For the Slater-determinant formulation, we discuss the
conversion of the YN interaction matrix elements from relative to
single-particle coordinates, the importance-truncation scheme that tailors the
model space to the description of the low-lying spectrum, and the role of the
redundant center-of-mass degrees of freedom. We conclude with a validation of
both formulations in the four-body system, giving converged ground-state
energies for a chiral Hamiltonian, and present a short survey of the $A\le7$
hyper-helium isotopes.
