The Symmetrical Defense is a chess

Chess

Chess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.Each player...

 opening

Chess opening

A chess opening is the group of initial moves of a chess game. Recognized sequences of opening moves are referred to as openings as initiated by White or defenses, as created in reply by Black. There are many dozens of different openings, and hundreds of named variants. The Oxford Companion to...

 that begins with the moves:

1. d4 d5

2. c4 c5

First described in print by Alessandro Salvio

Alessandro Salvio

Alessandro Salvio was an Italian chess player who is considered to be the unofficial world champion around the year 1600. He started an Italian chess academy in Naples, Italy, and wrote a book called Trattato dell'Inventione et Arte Liberale del Gioco Degli Scacchi, which was published in Naples...

 in 1604, the opening is often called the Austrian Defense because it was studied by Austria

Austria

Austria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...

n chess players including Hans Haberditz (c. 1901–57), Hans Müller (1896–1971), and GM Ernst Grünfeld

Ernst Grünfeld

----Ernst Franz Grünfeld , an Austrian grandmaster and writer specializing in opening theory, was for a brief period after the First World War one of the strongest chess players in the world....

.

The Symmetrical Defense is an uncommon variation of the Queen's Gambit Declined

Queen's Gambit Declined

The Queen's Gambit Declined is a chess opening in which Black declines a pawn offered by White in the Queen's Gambit:This is known as the Orthodox Line of the Queen's Gambit Declined...

.
It poses the purest test of Queen's Gambit

Queen's Gambit

The Queen's Gambit is a chess opening that starts with the moves:The Queen's Gambit is one of the oldest known chess openings. It was mentioned in the Göttingen manuscript of 1490 and was later analysed by masters such as Gioachino Greco in the seventeenth century...

 theory—whether Black can equalize by simply copying White's moves.
Most opening theoreticians believe that White should gain the advantage
and at best Black is playing for a draw

Draw (chess)

In chess, a draw is when a game ends in a tie. It is one of the possible outcomes of a game, along with a win for White and a win for Black . Usually, in tournaments a draw is worth a half point to each player, while a win is worth one point to the victor and none to the loser.For the most part,...

.

3. cxd5

White often replies 3.cxd5,
but other moves are playable and may lead to transpositions

Transposition (chess)

A transposition in chess is a sequence of moves that results in a position which may also be reached by another, more common sequence of moves. Transpositions are particularly common in opening, where a given position may be reached by different sequences of moves...

 into more well-known variations such as the Queen's Gambit Accepted

Queen's Gambit Accepted

The Queen's Gambit Accepted is a chess opening characterised by the moves:The Queen's Gambit is not considered a true gambit, in contradistinction to the King's Gambit, because the pawn is either regained, or can only be held unprofitably by Black...

 and the Tarrasch Defense

Tarrasch Defense

The Tarrasch Defense is a chess opening characterized by the moves:With his third move, Black makes an aggressive bid for central space. After White plays cxd5 and dxc5, Black will be left with an isolated pawn on d5...

.
After 3.cxd5 it is not advisable for Black to play 3...Qxd5, because either 4.Nf3 cxd4 5.Nc3 Qa5 6.Nxd4 or 5...Qd8 6.Qxd4 Qxd4 7.Nxd4 give White a big lead in development.
Instead, Black should play 3...Nf6 intending to recapture on d5 with his knight.
White should be able to maintain the advantage with either 4.Nf3 or 4.e4.
Possible continuations are 4.Nf3 cxd4 5.Nxd4 Nxd5 6.e4 Nc7 or 4.e4 Nxe4 5.dxc5 Nxc5 6.Nc3 e6.