  We begin with a brief overview of lattice calculations using chiral effective
field theory and some recent applications. We then describe several methods for
computing scattering on the lattice. After that we focus on the main goal,
explaining the theory and algorithms relevant to lattice simulations of nuclear
few- and many-body systems. We discuss the exact equivalence of four different
lattice formalisms, the Grassmann path integral, transfer matrix operator,
Grassmann path integral with auxiliary fields, and transfer matrix operator
with auxiliary fields. Along with our analysis we include several coding
examples and a number of exercises for the calculations of few- and many-body
systems at leading order in chiral effective field theory.
