it was built between 1894 and 1896, and originally was named after Emperor Franz Joseph (you can still see the original name on the eastern side of the bridge - on the left on this photo:photo ). it was exploded (along with all the other bridges in Budapest) as the German army left the country (at the same time the Russian 'relief' army occupied the country). it was the first bridge being rebuilt after the WWII and for propagandist reasons it was named 'Liberty' (to be thankful for the Russians...). it was completely renovated in 2008/2009 and recovered its original ornaments, etc.
short history in English: HERE longer version in Hungarian HERE, with some old photos, for example with one after it was exploded by the German Army.
Great photo - it's perfect from the symmetric view to the cyclist in the front. The best thing about the image, however, is the fog in the background, which makes the photo soft but mystical at the same time. All in all, this shot delivers a melancholic atmosphere to me and it represents the fast-paced urban life wonderfully.