The Parliament building was the royal residence from 1843 to 1924 when the Republic was proclaimed. (Monarchy was restored in 1935 after a military coup. It is a Greek tradition that monarchy and dictatorship are always in need for one another. It was abolished once and for all in 1975).
The building was designed and built by German architect Friedrich von Gärtner, known as the most famous architect of Bavaria under Ludwig I. He is known, among others, for Feldherrnhalle in Munich. It's interesting that all major buildings in Athens made before 1900, are of neoclassical style but were all designed by foreing architects, mostly German (Ziller, Gärtner etc) or Danish (Theophil Hansen).
The building houses the Parliament from 1929. Parts of it are open to the public.
Metro Station: Syntagma (Constitution Square), Blue or Red line.
Greek Parliament in Wikipedia