  The present work is connected with the investigation of the origin and
properties of compact astrophysical objects endowed with strangeness, with the
objective of finding out their relevance in the formation and evolution of the
universe. In the first part of the thesis, Chap.~1-3, we discuss a model,
proposed by us, to describe the propagation of small lumps of Strange Quark
Matter (SQM) or strangelets, through the Terrestrial atmosphere. The
theoretical results were found to be well correlated with exotic cosmic ray
events characterized by very low charge to mass ratio.
  In the next part, we have investigated the other end of the mass spectrum of
SQM. In Chap 5, we have developed an analytical expression for the
Chandrasekhar Limit of Strange Quark Stars. The limit is found to depend on the
fundamental constants (including the bag constant). In the last chapter we have
endeavored to show that the quark nuggets, surviving the quark-hadron phase
transition in the millisecond era of the early Universe can provide the
required closure density and can merge to form compact quark matter objects,
whose maximum mass would be governed by the formulation laid out in the
preceding chapter. We have also found that these Cold Dark Matter objects can
explain the recent astronomical observations of MACHOS by gravitational
micro-lensing techniques in the Large Magellanic clouds in the Halo of our
Galaxy.
