<p dir="ltr"><b>Tellurium (Te) stands out as an elemental narrow-bandgap semiconductor characterized by its distinctive chiral crystal structure. The interplay between fundamental symmetries and the topological properties of electrons has garnered significant attention in the scientific community. With its unique chiral crystal structure featuring three Tellurium atoms spiraling within a single unit cell, Tellurium offers a singular material system. This system provides an exceptional opportunity to explore the novel quantum and topological transport properties of electrons. Hydrothermally grown two-dimensional (2D) Te with a thickness of several nanometers gives us an opportunity to precisely control the carrier density and the carrier type in Te using gate voltage. In this dissertation, the spin-orbit coupling (SOC) of Te is quantitatively analyzed using the weak anti-localization effect. The strong SOC also gives rise to the Weyl point at the band edge of the conduction band. The topological nontrivial band structure of Te is characterized by a π phase shift in the Shubnikov-de Haas (SdH) oscillations. Due to the high mobility, the quantum Hall effect is measured with low spin and valley Landau levels controlled by an electric and magnetic field. Bilayer charge transferable quantum Hall states of Weyl fermions is observed in a wide Te quantum well. The topological phase transition from a semiconductor to Weyl semimetal under high pressure is studied up to 2.47 GPa. The chirality of 2D Te is separated by the hot sulfuric acid etching technique. The spin configuration and topological charge of the Weyl node exhibit a reversal in different chiralities, leading to an inverse in nonlinear responses, encompassing both electrical (nonreciprocal transport in the longitudinal direction and nonlinear planar Hall effect in the transvers direction) and optical phenomena (circular photogalvanic effect and circular photovoltaic effect). Our results unveil the topological nature of the Tellurium (Te) band structures, offering a promising avenue for controlling charge and spin transport within the chiral degree of freedom.</b></p>