This book attempts to give a discussion of the physics and current and potential applications of the self-focusing of an intense femtosecond laser pulse in a tra- parent medium. Although self-focusing is an old subject of nonlinear optics, the consequence of self-focusing of intense femtosecond laser pulses is totally new and unexpected. Thus, new phenomena are observed, such as long range lam- tation, intensity clamping, white light laser pulse, self-spatial ltering, self-group phase locking, self-pulse compression, clean nonlinear uorescence, and so on. Long range propagation at high intensity, which is seemingly against the law of diffraction, is probably one of the most exciting consequences of this new sub- eld of nonlinear optics. Because the intensity inside the lament core is high, new ways of doing nonlinear optics inside the lament become possible. We call this lamentation nonlinear optics. We shall describe the generation of pulses at other wavelengths in the visible and ultraviolet (UV) starting from the near infrared pump pulse at 800 nm through four-wave-mixing and third harmonic generation, all in gases. Remotely sensing uorescence from the fragments of chemical and biological agents in all forms, gaseous, aerosol or solid, inside the laments in air is demonstrated in the labo- tory. The results will be shown in the last part of the book. Through analyzing the uorescence of gas molecules inside the lament, an unexpected physical process pertaining to the interaction of synchrotron radiation with molecules is observed.