Как правильно сказать: at the home или at home? this is the cat или this is cat?

At home
the cat или a cat

1.At home
2.This is cat .

1) about 2000 years old

2) 8,982 millions

3) The British Museum

The Tower of London and Tower Bridge

Buckingham Palace 

Big Ben and Parliament

4) Napoleon Bonaparte

5) The National Gallery of Art – the nation's museum – preserves, collects, exhibits, and fosters an understanding of works of art.

6) Hyde Park is one of the largest parks in central London, England and one of the Royal Parks of London, famous for its Speakers' Corner. It is the largest of the four Royal Parks. The park is divided in two by the Serpentine Lake.

7) Buckingham Palace

8)

Trooping the Colour.

Churchill War Rooms.

Sir Keith Park Memorial.

Statue of the Earl Kitchener.

The Household Cavalry Museum.

Household Division.

Downing Street.

Banqueting House.

9) Big Ben

10) Over 3,300 people have been buried or commemorated at Westminster Abbey. This includes seventeen British monarchs including King Henry V and all the Tudors except for Henry VIII. Other notable people buried at Westminster Abbey include Isaac Newton, Edward the Confessor and Charles Dickens.

11) The Tower of London, officially Her Majesty's Royal Palace and Fortress of the Tower of London, is a historic castle located on the north bank of the River Thames in central London.

12) Today the Tower's ravens are one of the attractions for tourists visiting the City of London. 

Interesting places of St. Petersburg

Yuo should start the walk from metro station "Nevsky Prospekt" or "Gostiny Dvor".
Approximate itinerary covering the main attractions is:
Palace Square - St. Isaac's Square - The Bronze Horseman - The Palace Bridge -
then Vasilievsky island - the Peter and Paul fortress - the Cruiser "Aurora" - Troitsky Bridge - Summer Garden - the Savior on Blood.
It will take about five hours.
If you want to know the history and culture of the city ,enjoy the beauty of St. Petersburg, I would suggest you to pay more attention and time for such attractions as *** St. Isaac's Cathedral (from one to two hours)
*** The Hermitage (from four hours)
*** Peterhof (Petrodvorets) (about five hours)
*** Petropavskaya Fortress (about three-four hours)
One of the most important thing is  to see and enjoy drawbridges and to know what the "white nights" are.