Built around 1554 by the statesman Frands Brockenhuus. "Gothic renaissance" architecture, a peculiar mixture of the gothic middle ages and the new renaissance style. The latter can be recognised in the depressed round-arched windows, the round-arched blank arcading in the gables, the double string course between the high cellar and the ground floor.
The house is built of the large bricks introduced in Denmark in medieval times and known as "monk stones". It consists of a high cellar, two floors, watchman's passage and attic. Tower in the centre of the west side with main entrance and stairs, two corner towers on the opposite side, projecting friezes of round arches between the floors - all as at Hesselagergård and Borreby. Egeskov differs however in two respects. It is built as a double house, that is to say two long houses joined together; and it is a genuine water castle that rises directly out of the lake. It stands on oak piles and the walls rest on a stone plinth. There are countless arrow slits but many now bricked in. 
The gables were originally curved. They were changed in the 1880s to crowstep gables when the towers were heightened. The appearance before the changes can be seen here: 
From the south      From the north      (Pictures at Egeskov's web site ).

Here Rigborg Brockenhuus was imprisoned for life in the 1590s after she met Frederik Rosenkrantz and "They came so close that she was thereby delivered of a son" After five years her father died and her conditions were softened.

Denmarks oldest renaissance building, erected 1538-50 by chancellor Johan Friis. Built of large red brick on a granite plinth. The construction started as a late gothic defensive castle with moat, but by the end it had introduced many renaissance features, especially the highly decorated round gables inspired by the church architecture of Venice. Also decorative tops to the towers and depressed round-arched windows. Typical of the time are the blank arches below projecting brickwork and the watchman's passage at the top with machicolation for missiles and boiling liquid (as, for example, on Johan Friis' manor house Borreby on Sjælland).
Internally Hesselagergård is famous for its frescos in the Deer Room. 

Hans Christian Andersen connection

The west wing was built c.1600. Scored rendered facade with string course between the two floors. Projecting square tower. Curved renaissance gables later replaced with crowstep gables. The south and north wings in classical style added in the 1780s.

This important castle originally had four wings but only the west wing and east tower remain. First built around 1265. Enlarged and changed in the middle of the 16th century when the west wing was lengthened and heightened with a walkway and round-arched frieze.
The Danish kings held their state counsels here from 1282 to 1413 in accordance with the agreement which the kings had to sign upon their accession.

A most attractive manor house complex by the sea consisting of an artificial  lake with the baroque main house of 1678 at one end and rococo buildings of 1754-5 on the other sides.
The original house was built by King Christian 4th for his son Valdemar, hence the name. It was destroyed by the Swedes in 1658 and rebuilt in 1678-80 in the baroque style by the new owner Niels Juel. Reddish brown walls on a granite plinth, cellar, two floors, attic with hipped roof and many dormer windows.  Main entrance in the middle with a wide staircase. Projecting wings on the garden side, the southern wing containing the chapel on two floors. The tall neo-gothic chapel windows inserted as part of the restoration of 1880 broke the symmetry of the facade. 

The architect G.D. Tschierscke added the new buildings to the complex in 1754-5. A curved wall links the main building at both ends to rococo gatehouses. These are rendered in white with yellow detailing and a clock tower in copper on a black, glazed tile roof. East of the gatehouses are long narrow estate buildings. At the far end by the sea lies an elegant rococo facing the main house across the lake.

The entrance hall from 1678. Marble floor in back and white panels. The rococo decoration is from the 1750s (over the doors and on the ceilings).

Valdemars Slot website