The study of the cosmos has mesmerized humans since many centuries. Our present knowledge of the Universe is based on the standard Big Bang theory. The detection of the cosmic microwave background (CMB) is one of the strongest evidences of the Big Bang model. The isotropy of the CMB shows that the Universe is very isotropic on the large scales. The CMB also shows a spectrum of very small density fluctuations that form the seeds for structures in the Universe. The formation of the first objects (i.e., first stars and quasars) at the end of dark ages is an outstanding issue in the modern cosmology. They were formed when the Universe was about 400 million years old as shown in the figure 1. During the past decade, the study of primordial objects has gained a lot of interest but still many questions remain unanswered about their formation. In this thesis, we have addressed some of the key questions pertaining to the formation of the first objects. It is generally believed that structures in the early Universe are formed out of small density perturbations as a result of a gravitational instability. These perturbations are produced due to quantum fluctuations in the gravitational potential during the early Universe. They collapse under self-gravity to form small structures. They merge with each other to form bigger structures and this scenario is called hierarchical scenario of structure formation. The growth of structures depends upon the contents of the Universe. The Universe comprises 70% dark energy which is responsible for its expansion. It was realized in early 80s that most of the matter in the Universe is not comprised of atoms. Rather, non-luminous source of gravity was found to be essential to explain the rotation curves of galaxies which we call dark matter. The Universe comprises 23% dark matter and only 4% atoms that is the model known as Lambda cold dark matter (LCDM). In the very begining, density perturbations are small. They grow linearly and equations describing their evolution can be solved analytically. As density perturbations grow non-linear analytical solutions become too complex. It necessitates the use of numerical simulations to study their growth. We have performed numerical simulations to study the formation of the first objects. We have used the FLASH code which is freely available and is well suited for our problem. It can run on many parallel systems.