This dissertation describes an attempt to detect water in the atmosphere of the extrasolar planet HD 209458b using transit spectroscopy. It first discusses the importance of water detection and reviews the state of knowledge about extrasolar planets. This review discusses the main statistical trends and describes the detection methods employed to this date. The importance of the transiting planets and the many measurements of the known ones are also discussed.A radiative transfer model designed and built specifically for this project predicts, given a planetary temperature/pressure/composition profile, the dependence in wavelength of the stellar spectrum modulation due to a transiting planet. A total of 352 spectra around 1.8 µm were obtained on four nights (three in transit) of observations on August 3-4, September 26, and October 3 of 2002 using ISAAC at the Very Large Telescope.Correlating the modeled modulation with the infrared spectra yields a nondetection of water in the atmosphere of HD 209458b. It is found that the nondetection is due to an unfortunate choice of observing parameters and conditions that made it impossible to reach the required sensitivity. Nonetheless, the results are scaled with synthetic spectra to place strong limits on the planetary system configurations for which the observing parameters and telluric conditions would have yielded a successful detection. None of the 10 other known transiting planets would be detectable with the choice of parameters and conditions for this observation.A quantitative model of an improved observing strategy for future observations of this kind is developed. The improvements include: airmass and timing constraints, the simultaneous observation of a calibrator star, and a new method to find the optimal wavelength range.The data-reduction process includes several original techniques that were developed during this work, such as a method to remove fringes from flat fields and several methods to correct for telluric absorption, among others.