The evolution of the core rotation rate of red giant stars is a key parameter in understanding the stellar behavior in the late phases of stellar evolution. Thanks to the mixed-dipole modes, we can constrain the core rotation and internal rotational gradient as a star advances through the red-giant phase. This master thesis presents a pipeline performing a classical seismic analysis of the power-spectral density of oscillating red-giant stars and identifying the period spacing and coupling coefficient to describe the mixed mode pattern precisely. Using the MESA stellar evolution and the GYRE stellar oscillation codes, we calculate the representative models of the selected stars and derive the rotational kernels for the dipole modes. From the semi-automatically detected rotational splittings and the assumption of a two-shell rotation model for the stars, we constrain the rotational gradient in three different stages of the red-giant evolution.