We introduce a passive common-path interferometer to replace Michelson interferometers in Fourier transform spectroscopy. Our device exploits birefringence to introduce a highly accurate delay between two orthogonal polarization components by continuously varying the material thickness. Thanks to its inherent delay stability and reproducibility, it can be used even for short wavelengths (down to ~200nm) without the need for any active control or position tracking. We first demonstrate its performances in linear spectroscopy, by implementing a spectrometer and a spectrophotometer. We then extend its use to nonlinear spectroscopy and, in combination with lock-in detection at MHz modulation frequencies, illustrate its application to pump-probe spectroscopy with high sensitivity (ΔT⁄T<3·10-6 in 1-s integration time) and broad spectral coverage (>500nm) and to broadband stimulated Raman scattering microscopy in the CH stretching\ud
region