In this study the fundamentals of structural dynamics and system identification have been studied. Then some fundamental parameter estimation algorithms in the literature are provided. These algorithms will be applied to an experimental and an artificial system to extract their structural properties. Consequently, the main objective of this study is constructing the mathematical model of a structure by using only the measurement data.To process measurement data, three fundamental modal analysis algorithms are examined. Least-Squares Complex Exponential(LSCE), Eigensystem Realization Algorithm( ERA) and Polyreference Frequency Domain(PFD) algorithms are implemented in MATLAB environment. We applied these algorithms to artificial and experimental data, then we compared the performance of these algorithms. State estimation for linear dynamical systems have also been studied, and details of the Kalman filter as a state estimator are provided. Kalman filter as a state estimator has been integrated with the ERA algorithm and the performance of the Kalman-ERA is provided.