Completed in 1956, the Vidhana Soudha is built in a "Neo-Dravidian" style that mixes Dravidian temple elements with Indo-Saracenic domes. It houses the Karnataka Legislative Assembly and Council and many government offices.
The building is lit up on Sundays, public holidays and special occasions. Guided tours of the interior have been offered from time to time, so check current arrangements before you go. Opposite stands the red Attara Kacheri, the High Court of Karnataka.
Further reading: Vidhana Soudha on Wikipedia.