Pulse shaping is the technique which controls the ultra-short pulse shape, and it became of great technological interest because of its potential applications in laser pulse compression, digital communications, microscopy etc. We demonstrate the idea of pulse-shaping technique and pulse propagation with low energy losses in a resonant linear absorbing medium. This thesis presents the results of a study of the propagation of Gaussian and hyperbolic secant ultrashort chirped and chirp-free pulses in homogeneously and inhomogeneously broadened resonant linear absorbers. Changes to the pulse shape and energy loss factor are presented as the pulse propagates in the absorber. The Fast Fourier method is used to numerically determine both the normalized intensity profile and the pulse spectrum. Our results show that, for pulse durations shorter than the relaxation time, chirped pulses in absorbing media obey the area theorem, with their shape changing with the propagation distance. Simulation results of the spectra of chirped pulses clearly show the burning of a spectral ’hole’ as the pulse propagates, with the pulse energy pushed away towards the wings. When compared to chirp-free pulses, chirped pulses reshape faster and develop wings in their tail due to initial phase modulation. Simulation results of the energy loss factor show that chirped pulses propagating in resonant linear absorbers sustain less energy losses than do chirp-free pulses. A comparison of chirped secant and Gaussian pulses shows that secant pulses propagate with lower energy losses. Analytic solutions are presented for long-distance asymptotic expressions of initial rms spectral bandwidth as well as for the attenuation factor of chirped Gaussian pulses. These analytical results are in agreement with numerical simulations. The comparison of energy losses of short chirped Gaussian pulses and long pulses of any profile in linear absorbers is also discussed in the thesis.