High penetration of inverter-based resources (IBRs) in modern power grids reduces system inertia and short circuit levels, emphasizing the need for fast and reliable transmission line protection to maintain grid stability. This thesis presents novel algorithms to improve the speed and reliability of line distance protection and faulted phase selection. This thesis explores two new approaches to improve the speed of line distance protection. The first algorithm uses the dynamic phasor model of a transmission line and the dynamic phasors of the measured currents and voltages to estimate the impedance from the relay location to the fault point. The second line protection algorithm uses the Clarke equivalent networks of a transmission line and the Clarke components of instantaneous incremental currents to estimate the inductance and the resistance from the relay location to the fault point and compare them against the reach settings. The algorithm employs least squares estimation to determine fault loop inductance and resistance. This algorithm is faster than the traditional phasor-based protection algorithms and remains consistent irrespective of fault location and fault resistance while maintaining equal or better dependability and security. The thesis also examines the problem of determining fault type and faulted phases and proposes two new algorithms. The first algorithm uses current transients in a selected frequency band. A set of indices is computed considering various ratios of the rate of change of the Clarke components of these bandpass-filtered currents. The algorithm makes the decisions based on the values of these indices calculated within a short time window of 0.75 ms after detecting a fault. The second algorithm determines the faulted phases based on the ratios of the rate of change of instantaneous incremental currents computed using a pair of phases at a time, offering simpler implementation and reliable identification within 6 ms. The performance of the proposed algorithms was validated through extensive simulation studies. The new protection algorithms presented in this thesis can improve the speed of operation of transmission line protection without compromising reliability and requiring expensive highly specialized hardware.