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Charged particles gyrate around magnetic field lines, a property that is exploited to confine plasma in magnetic confinement fusion devices. Typically, the gyroradius is small compared to the system size and thus the gyromotion can be averaged out. The resulting charged particle motion closely follows a magnetic field line. At the edge of fusion devices, the magnetic field usually impinges on a wall at a shallow angle. A boundary layer forms in which the plasma density changes over a characteristic distance from the wall of the order of the ion gyroradius, as ions are absorbed during their gyromotion. This boundary layer is called magnetic presheath, and is typically collisionless and quasineutral. Importantly, the electric field in this region distorts the ion gyro-orbits, making them non-circular and thus affecting the ion density profile. Solving the magnetic presheath amounts to obtaining the self-consistent electric field for which the net charge density is zero. In this thesis, I assume a small magnetic field angle and small gradients parallel to the wall to develop an asymptotic theory for the magnetic presheath, which is used to obtain the ion density. The small, yet crucial, contribution of the part of the orbit near the wall is included. To demonstrate the theory for a case without any gradients parallel to the wall, I calculate numerically the self-consistent electrostatic potential by assuming the electron density to be a Boltzmann distribution. The model is used to study the dependence of magnetic presheath characteristics on magnetic field angle and ion temperature. The distribution function of ions that have traversed the magnetic presheath is obtained, which is important to predict the amount of sputtering and erosion at the wall of a fusion device.