  The highlights and main results of this work can be summarized as follows :
(1) The energy per nucleon of cold nuclear matter, derived by us using chiral
sigma model, is in good agreement with the preliminary estimates inferred from
heavy-ion collision data in the density range between one to four times the
nuclear saturation density. (2) For a system of high density nuclear matter,
based on the chiral sigma model, we find that a strict first order phase
transition to quark matter is not favoured. This does not, of course, preclude
a phase transition of second order. However, we have not investigated the
latter problem. (3) The mass formulae for finite lumps of strange quark matter
with $u,~d$ and $s$ quarks and non-strange quark matter are derived in a
non-relativistic approach, taking into account the finite size effects such as
surface and curvature. We find that there is a good possibility for the
formation of metastable strangelets of large mass detectable in experiment. (4)
The maximum mass for stable neutron stars predicted by our equation of state
for ($n,~p,~e$) matter is 2.59 times the solar mass. The corresponding radius
($R$), crustal length ($\Delta$) and surface red shift ratio ($\alpha$) are
14.03 $km$, 1.0 $km$ and 0.674 respectively. The maximum moment of inertia is
$4.79 \times 10^{45}~g~cm^{2}$. These suggest that our equation of state for
neutron star matter is comparatively ``stiff". (5) The neutrino emissivity from
two and three flavour quark matter is numerically calculated and compared with
the result given by Iwamoto. We find that the emissivity is smaller than
Iwamoto's result by about two orders of magnitude when
$p_{f}(u)+p_{f}(e)-p_{f}(d(s))$ is comparable to the temperature. We attribute
this to the severe restriction imposed by momentum conservation on the phase
