This paper presents the electronic properties of a graphite bilayer, focusing on Landau level (LL) degeneracy and the quantum Hall effect (QHE). The authors derive an effective two-dimensional Hamiltonian for low-energy electronic excitations in a graphite bilayer, which describe chiral quasiparticles with a parabolic dispersion and a Berry phase of $2\pi$. The LL spectrum consists of almost equidistant groups of four-fold degenerate states at finite energy and eight zero-energy states. This leads to a Hall conductivity dependence on carrier density, $\sigma_{xy}(N)$, which exhibits plateaus at integer values of $4e^2/h$ and a "double" $8e^2/h$ step between the hole and electron gases across zero density, in contrast to $(4n+2)e^2/h$ sequencing in a monolayer. The bilayer is modeled as two coupled hexagonal lattices with inequivalent sites A, B and $\tilde{A}, \tilde{B}$ in the bottom and top layers, arranged in a Bernal (A-B) stacking. The low-energy states are described by a Hamiltonian $\hat{H}_2$, which includes terms for intra- and interlayer hopping. The effective Hamiltonian $\hat{H}_2$ operates in the space of two-component wave functions describing electronic amplitudes on A and $\tilde{B}$ sites and is applicable within the energy range $|\varepsilon| < \frac{1}{4}\gamma_1$. The zero-energy LL in a bilayer is 8-fold degenerate, due to spin and valley degeneracies, in contrast to the 4-fold degeneracy of other bilayer states and the 4-fold degeneracy of all LLs in a monolayer. The LL spectrum in a bilayer determines a specific sequencing of plateaus in the density dependence of the QHE conductivity $\sigma_{xy}(N)$, which is distinguishably different from that of Dirac-type quasiparticles in a graphite monolayer and of non-chiral carriers in conventional semiconductor structures. The authors show that quasiparticles in a graphite bilayer exhibit a peculiar LL spectrum, with chiral quasiparticles exhibiting a Berry phase $2\pi$, and a double-degenerate zero-energy LL incorporating two different orbital states with the same energy. The structure and degeneracies of the LL spectrum in a bilayer determine the specific sequencing of plateaus in the density dependence of the QHE conductivity $\sigma_{xy}(N)$, which is different from that of Dirac-type quasiparticles in a monolayer and of non-chiral carriers in conventional semiconductor structures. The authors also show that the zero-energy LL in a bilayer is 8-fold degenerate, in contrast to the 4-fold degeneracy of other LLs in a monolThis paper presents the electronic properties of a graphite bilayer, focusing on Landau level (LL) degeneracy and the quantum Hall effect (QHE). The authors derive an effective two-dimensional Hamiltonian for low-energy electronic excitations in a graphite bilayer, which describe chiral quasiparticles with a parabolic dispersion and a Berry phase of $2\pi$. The LL spectrum consists of almost equidistant groups of four-fold degenerate states at finite energy and eight zero-energy states. This leads to a Hall conductivity dependence on carrier density, $\sigma_{xy}(N)$, which exhibits plateaus at integer values of $4e^2/h$ and a "double" $8e^2/h$ step between the hole and electron gases across zero density, in contrast to $(4n+2)e^2/h$ sequencing in a monolayer. The bilayer is modeled as two coupled hexagonal lattices with inequivalent sites A, B and $\tilde{A}, \tilde{B}$ in the bottom and top layers, arranged in a Bernal (A-B) stacking. The low-energy states are described by a Hamiltonian $\hat{H}_2$, which includes terms for intra- and interlayer hopping. The effective Hamiltonian $\hat{H}_2$ operates in the space of two-component wave functions describing electronic amplitudes on A and $\tilde{B}$ sites and is applicable within the energy range $|\varepsilon| < \frac{1}{4}\gamma_1$. The zero-energy LL in a bilayer is 8-fold degenerate, due to spin and valley degeneracies, in contrast to the 4-fold degeneracy of other bilayer states and the 4-fold degeneracy of all LLs in a monolayer. The LL spectrum in a bilayer determines a specific sequencing of plateaus in the density dependence of the QHE conductivity $\sigma_{xy}(N)$, which is distinguishably different from that of Dirac-type quasiparticles in a graphite monolayer and of non-chiral carriers in conventional semiconductor structures. The authors show that quasiparticles in a graphite bilayer exhibit a peculiar LL spectrum, with chiral quasiparticles exhibiting a Berry phase $2\pi$, and a double-degenerate zero-energy LL incorporating two different orbital states with the same energy. The structure and degeneracies of the LL spectrum in a bilayer determine the specific sequencing of plateaus in the density dependence of the QHE conductivity $\sigma_{xy}(N)$, which is different from that of Dirac-type quasiparticles in a monolayer and of non-chiral carriers in conventional semiconductor structures. The authors also show that the zero-energy LL in a bilayer is 8-fold degenerate, in contrast to the 4-fold degeneracy of other LLs in a monol