A transiting extrasolar planet sequentially blocks off the light <br /><br /><br />
coming from the different parts of the disk of the host star in a time <br /><br /><br />
dependent manner. Due to the spin of the star, this produces an <br /><br /><br />
asymmetric distortion in the line profiles of the stellar spectrum, <br /><br /><br />
leading to an apparent anomaly of the radial velocity curves, known as <br /><br /><br />
the Rossiter -- McLaughlin effect. We derive approximate but accurate <br /><br /><br />
analytic formulae for the anomaly of radial velocity curves taking <br /><br /><br />
account of the stellar limb darkening. Then we show the first <br /><br /><br />
discovery of the misalgnment angle between the spin axis of the host <br /><br /><br />
star and the orbital axis of the planet, HD 209458b. We also describe <br /><br /><br />
our recent theoretical modeling of photometric and spectroscopic <br /><br /><br />
signatures of rings around transiting extra-solar planets.