Swastika or Swastik (Sanskrit: svástika स्वस्तिक; "well-being"; German: hakenkreuz; "hooked cross") is an ancient symbol usually associated with Eastern religions or as decorative art as early as the Bronze Age; its use in Germany as an emblem for the Nazi Party made it one of the most recognizable symbols of hatred in history.
The historical swastik is an even cross based on the dimensions of a square, with the arms of the cross bent at right angles either clockwise or counter-clockwise. Usually most religious instances of the swastika are based on the dimensions of a square; while Nazi use has it based on the dimensions of a diamond shape (square tilted @ 45 degrees). 
Found in ancient sites world-wide, it has been surmised that it was used to symbolize the rotation of the sun or creation, as the arms give the impression of continual rotation. Heinrich Schliemann found images of the swastika painted on pottery recovered from the ruins of Troy during his expeditions there in the 1870's. As a religious symbol, the swastika has powerful symbolic meanings in the Buddhist, Jain, and Hindu religions. As such, it was adopted by Rudyard Kipling as part of the logo on most of his books.
Adolf Hitler adopted the swastika as the emblem for his Nazi Party; it was emblazoned in a white circle centered on a red field for his flag; the party flag became the national flag soon after Hitler took power after 1933. The mass killings of Jews and other minorities by the Nazis occurred under swastika banner through the end of World War II in 1945, and since then the swastika has come to symbolize extreme hate. It is still used as such a symbol today by neo-Nazis in Europe and North America, as well as white-supremacist and other hate groups.