Congruent $LiNbO_3$ crystals with doped Mg and codoped with Mn or Fe were grown by the Czochralski method. It is known that the physical properties of $LiNbO_3$ depend strongly on the addition of Mg and transition metals. This is established by studying the following properties; XRD patterns, the phase transition temperature, energy of the fundamental absorption edge, the shape of the absorption band of the $OH^-$ vibration and lines of the ESR of $Fe^{3+},; Mn^{2+}$. The position of the UV absorption edge and the shape and peak point of the absorption band of the $OH^-$ vibrational band changed monotonously up to a critical concentration of $Mg^{2+}$ ions. The mechanism of the incorporation of Mg ions changes at this concentration. The transition temperature was estimated by measuring the dielectric temperature behavior up to $1230^{circ}C$ in a frequency range of 100Hz to 10MHz. EPR of $Mn^{2+};and; Fe^{3+}$ ions were employed to investigated the Mg doping effects in the $LiNbO_3$ crystal. The increase of linewidths and the asymmetry of signals were observed in all crystals. New signals of $Fe^{3+}$ arising from the new centers were observed I the heavily Mg-doped crystals.