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In this dissertation,the detection of shallow levels in semiconductor by Admittance Spectroscopy has been studied.In the first part of this dissertation,the theoretical calculation about the detection of shallow levels in semiconductor by Admittance Spectroscopy has been studied.A theoretical simulation of Admittance Spectroscopy(AS) has been conducted to determine a method to analyze shallow levels in semiconductors.It is quite different with that usually used to detect deep levels in semiconductors.Through analyzing the simulated AS curves given by a unified equivalent circuit model taking into account the Schottky barrier capacitance and the substrate resistance at the temperature range from 20K to 60K,an approximate method(ω_r= A·exp(-Ea/k₀T))to detect shallow levels has been determined.Besides,the shallow levels of Boron and Phosphor in p-type and n-type silicon have been measured by this approximate method,and the results indicated that the approximate method works quite well.In the second part of this dissertation,the research about the Zeeman splitting of shallow levels in semiconductor by Admittance Spectroscopy has been studied. Usually,Zeeman splitting has been detected by optical means instead of electrical means such as AS.Here,AS has been introduced to detect the activation energy measured between the ground state of shallow levels and the valence band of P-Si as magnetic field varies while the activation energy can hardly be detected by optical means because the absorption edge can hardly be located to get the activation energy. In detecting shallow levels changed with magnetic field,AS has its advantages such as convenient measurement and not very low temperature compared with traditional optical means.