  We study various properties of bosons in two dimensions interacting only via
onsite hardcore repulsion. In particular, we use the lattice spin-wave
approximation to calculate the ground state energy, the density, the condensate
density and the superfluid density in terms of the chemical potential. We also
calculate the excitation spectrum, $\omega({\bf k})$. In addition, we performed
high precision numerical simulations using the stochastic series expansion
algorithm. We find that the spin-wave results describe extremely well the
numerical results over the {\it whole} density range $0\leq \rho \leq 1$. We
also compare the lattice spin-wave results with continuum results obtained by
summing the ladder diagrams at low density. We find that for $\rho \leq 0.1$
there is good agreement, and that the difference between the two methods
vanishes as $\rho^2$ for $\rho \to 0$. This offers the possibility of obtaining
precise continuum results by taking the continuum limit of the spin-wave
results for all densities. Finaly, we studied numerically the finite
temperature phase transition for the entire density range and compared with low
density predictions.
