This paper reports the discovery of a two-dimensional (2D) gas of massless Dirac fermions in graphene, a single atomic layer of carbon arranged in a honeycomb lattice. Unlike conventional materials, graphene's electrons behave as relativistic particles with zero mass and an effective speed of light of approximately $10^6$ m/s. The electronic properties of graphene are governed by the Dirac equation, leading to unique phenomena such as the integer quantum Hall effect occurring at half-integer filling factors, a minimum conductivity of $e^2/h$, and Shubnikov-de Haas oscillations with a phase shift of $\pi$ due to Berry's phase. Graphene was synthesized using micromechanical cleavage of graphite and characterized using various microscopies. The study revealed that graphene exhibits linear conductivity with gate voltage, high carrier mobility, and unique quantum oscillations. Shubnikov-de Haas oscillations in graphene show a linear dependence of the fundamental frequency $B_F$ on carrier concentration $n$, indicating a quadruple degeneracy. The cyclotron mass $m_c$ of carriers in graphene is found to be proportional to the square root of $n$, and the data supports the linear dispersion relation $E = \hbar k c_*$, where $c_* \approx 10^6$ m/s. The half-integer quantum Hall effect in graphene is explained by the existence of zero-energy Landau states and the Atiyah-Singer index theorem. The unique electronic properties of graphene, including its relativistic-like spectrum and the absence of localization effects, allow for the study of quantum electrodynamics and phenomena relevant to cosmology and astrophysics. The minimum conductivity of $e^2/h$ is an intrinsic property of Dirac fermions, and the observed behavior is consistent with theoretical predictions. The study highlights the importance of graphene as a platform for exploring exotic quantum phenomena in condensed matter physics.This paper reports the discovery of a two-dimensional (2D) gas of massless Dirac fermions in graphene, a single atomic layer of carbon arranged in a honeycomb lattice. Unlike conventional materials, graphene's electrons behave as relativistic particles with zero mass and an effective speed of light of approximately $10^6$ m/s. The electronic properties of graphene are governed by the Dirac equation, leading to unique phenomena such as the integer quantum Hall effect occurring at half-integer filling factors, a minimum conductivity of $e^2/h$, and Shubnikov-de Haas oscillations with a phase shift of $\pi$ due to Berry's phase. Graphene was synthesized using micromechanical cleavage of graphite and characterized using various microscopies. The study revealed that graphene exhibits linear conductivity with gate voltage, high carrier mobility, and unique quantum oscillations. Shubnikov-de Haas oscillations in graphene show a linear dependence of the fundamental frequency $B_F$ on carrier concentration $n$, indicating a quadruple degeneracy. The cyclotron mass $m_c$ of carriers in graphene is found to be proportional to the square root of $n$, and the data supports the linear dispersion relation $E = \hbar k c_*$, where $c_* \approx 10^6$ m/s. The half-integer quantum Hall effect in graphene is explained by the existence of zero-energy Landau states and the Atiyah-Singer index theorem. The unique electronic properties of graphene, including its relativistic-like spectrum and the absence of localization effects, allow for the study of quantum electrodynamics and phenomena relevant to cosmology and astrophysics. The minimum conductivity of $e^2/h$ is an intrinsic property of Dirac fermions, and the observed behavior is consistent with theoretical predictions. The study highlights the importance of graphene as a platform for exploring exotic quantum phenomena in condensed matter physics.