In the monography, the modern attitude determination methods of nanosatellites are presented. For attitude determination, vector measurement and extended Kalman filter (EKF) based methods are taken into consideration. As attitude sensors, magnetometers, sun sensors and horizon sensors are used. The different types of single-frame attitude determination methods are examined and compared by simulation results of satellite attitude dynamics. For comparison the absolute errors, error variances and Root Mean Square (RMS) errors of the calculated attitude angles are used. EKF algorithms for the attitude and rate estimation based on only magnetometer measurements and on magnetometer and sun sensor measurements are designed and investigated. The attitude kinematics and dynamics of the nanosatellite are simulated using MATLAB software, and effectiveness of each designed attitude determination method is analyzed.